Become a Patent Attorney
To become a patent agent (markedly distinct from a patent attorney), one must pass the United States Patent and Trademark registration examination of which the required passing score is 70 correct answers out of 100 multiple choice questions. A law degree is not necessary to take the exam, nor are law courses; however the US patent office does require a background in one of the "hard sciences" - in other words, a B.A. in chemistry, physics, biology or engineering. To become a patent attorney, namely a registered patent attorney, one must have studied law.
A patent law firm recruiter will most likely seek out registered patent attorneys rather than patents agents to join their patent law practice.