The short answer is yes, depending on whether your instructor has okayed it for this particular assignment.
Satire can be very informal and can certainly be written from the first person perspective. It can also follow all the rules of a formal paper, consider the paper written by a physics professor that was a form of satire of English critical writing. Once it was published he declared it to be a fraud, but it was very formal and followed all the rules of course.
One of the most famous and often considered the best examples of satire, Jonathan Swift's "A Modest Proposal" was written from the first person perspective and thus included the use of I.