From the UC Berkeley library website:
California state university and community college students
You must be currently enrolled to purchase a six-month Library card. Proof of eligibility is your current student ID and proof of current registration. The fee is $25. Please review application and privileges details.
California state university and community college full-time faculty
You may obtain a Library card by presenting a letter on school letterhead, signed by your department chair, confirming your full-time affiliation with your school and a California driver's license. Please review application and privileges details.