Much like compatibilism, Buddhism acknowledges the existence of volition, which in the latter is seen as something that arises as part of the conscious stream of experience. And much like compatibilism, Buddhism acknowledges that just like every other entity in reality, volition is conditioned on a whole host of other entities. If we name the conditions that give rise to volition something like "antecedent causes", or "current circumstances plus the laws of nature", then we tread dangerously close to hard determinism. For what good is volition if you had no hand in choosing it freely? As Arthur Schopenhauer concisely stated, "Man can do what he wills but he cannot will what he wills".
At this point, I could argue semantics and say that compatibilism offers nothing new in the way of free will, except for a redefinition. Instead of arguing for free will's existence, compatibilism simply redefines "acting freely" from choosing an action out of a list of potentials without any coercion, to choosing an action based on a volition that was entirely coerced. Before I conclude this digression, let me illustrate this in a more poignant way.
First consider how hard determinism views the world:
... -> p_(n-2) -> p_(n-1) -> p_n -> p_(n+1) -> p_(n+2) -> ...
In hard determinism, we are the nth state of the universe in a long chain of states (possibly infinite). Each state follows directly from its predecessor and the laws of physics. Thus every state is completely determined by its antecedents, and thus every future action of yours is already written in stone. You might be tempted to throw quantum mechanics into this discussion, but doing so would not actually amount to anything. Maybe the result would be that the chain branches and isn't linear, or that there are random events--in either case, there's still no personal control over these factors, so you're not granted any additional freedom.
Now consider what compatibilism offers:
... -> p_(n-2) -> p_(n-1) -> V -> p_n -> p_(n+1) -> p_(n+2) -> ...
V represents in this case our volition. Note that compatibilists do not claim that volition is in any way special, that it is somehow immune from the causal chain upon which it rests. Compatibilists fully acknowledge that the state of volition is just like any other state of the universe, it is completely determined. Moreover, compatibilists do not argue that volition transitions into present action in any special way either; they will admit that action proceeds from volition in a manner prescribed by the laws of physics. The only thing that differs is that compatibilists have given a name to the direct antecedent cause of an agent's action (volition), and that an agent can act on that cause (forced to act by that cause would be more accurate). What I mean by that last aside is that if you have the volition to do something, you're going to do it, you're determined to.
Bringing this back to Buddhism, as already stated above, the volition arises in consciousness, and is dependently originated. That much we can agree on, but precisely what this means for free will is left somewhat ambiguous, at least for those interpreting the meaning from within a Buddhist context. To me, it seems overwhelmingly a deterministic view at best (if free will is defined in more traditional terms like the one given above), and a compatibilist view at worst (but as I showed above, this is just a semantic game that degrades into determinism when scrutinized).
There are a few reasons why Buddhism might want to incorporate free will into its doctrines. For one, it allows karma to make sense. How can karma be retributive if no one is truly responsible for their actions? Moreover, how is one's afterlife determined if not by the consequences of their freely chosen actions? Since I don't believe in karma or reincarnation, I don't really feel compelled to make any arguments for them, but they aren't hard to think of. For example, there's no reason why karma has to be fair if it's a blind force of nature. Or perhaps it's more like human judicial systems, wherein punishments are meant to discourage bad behavior, and rewards to promote good ones, regardless of whether the behaviors are conditioned or not.
On the other hand, I feel that there are far more reasons why Buddhism should incorporate hard determinism into its doctrines instead. For one, it would promote far more compassion. By letting go of free will, it suddenly no longer makes sense to hate a person for any reason. The mindset of "don't hate the sinner, hate the sin" instantly makes sense. We can hate the act of murder, but love the murderer because we compassionately understand that their actions were determined by forces entirely out of their hands (note that this doesn't mean crimes should go unpunished, refer to where I wrote about the human judicial system). Even oddballs with socially unacceptable personalities are seen in a better light. I.e., Since you didn't pick your horrible personality, how can I hate you for it?
No matter where or who we look at with our free-will-free-lenses on, we see compassion, acceptance, and understanding. Naively, some might take this to mean passiveness and misguided tolerance. But that certainly does not logically follow from what I've said so far. If in some part of society an anti-social behavior arises, we still have the tools to recognize and address it, regardless of the fact that both the initial behavior and our reaction to it is conditioned. Ill behaviors, can and still should be corrected.
As a conclusion, I'll leave you with a video of Sam Harris laying down an airtight argument for hard determinism, and making some of the same points about compassion as I have (though far more eloquently).