It is an interesting question, and one which I don't think has a straightforward or easy answer. How you address this question would be shaped by how you weigh the various factors that contributed to Caesar's death. Some of these were within Caesar's ability to control, and some of them were not.
First of all, be aware that there existed a conspiracy to bring about Caesar's death. These events were manufactured by outside forces. Furthermore, there is Cassius's manipulations of Brutus himself, using lies and deception to bring Caesar's friend into the conspiracy against Caesar. When answering a question such as this one, you need to account for the fact that Caesar was assassinated. Thus, I don't think you can argue that his death was entirely self-caused. The answer is murkier than that.
On the other hand, however, there are two additional factors to be aware of. First of all, even though Cassius manipulates Brutus to bring him into the conspiracy, the fundamental charge against Caesar—that he is a would-be tyrant—does seem to be valid. Indeed, note that they are able to lure Caesar into the senate with the promise of giving him a crown. Caesar does seem to act out of a desire to dominate the Roman State.
Furthermore, be aware that Caesar is given warning ahead of time, first by the soothsayer in act 1, scene 2, and later by his wife, Calpurnia. Omens play a major role in Julius Caesar, and Caesar himself takes those omens seriously. In act 2, scene 2, Caesar is even temporarily convinced by his wife to remain home that fateful day, though he has a later change of heart. From this perspective, I don't think you can say that he was entirely responsible for his own destruction, given that he was the target of a conspiracy. However, his own mindset, decisions, and desire for power certainly played a role in his demise.