Here are a couple of links to get you started in finding a new rental that accepts cats.
(Note: The CRC is not affiliated with or officially endorsing any of these sites; they are for information only.)
http://www.mynewplace.com/ep/pet-friendly-apartments
https://www.peoplewithpets.com
https://www.zillow.com/san-jose-ca/pet-friendly/
https://www.apartmentlist.com/ca/santa-clara/c/pet-friendly-apartments-for-rent
https://www.trulia.com/for_rent/San_Jose,CA/cats,lg_dogs,sm_dogs_pets/
https://www.apartments.com/san-jose-ca/pet-friendly/
https://www.apartmentguide.com/apartments/California/San-Jose/pet-friendly-4lh/