Is it a good idea to apply to the same professor again after having been rejected the year before?
It very much depends on why you were rejected.

For example, a year ago, it's possible the professor couldn't fund a student. Or there were limited spots, and someone else urgently needed a student. Or they were just getting a project going, and didn't want to add another person into their lab.

All of those are circumstances where it might be possible to revisit your application.

If you don't know the reason, you might still try. After all, if you don't apply functionally the answer is "No".