Do I need to take SAT to transfer to a University from a college?

No, you do not have to take the SAT. You can bypass the SAT, and still attend a city college for the next 2 years, then transfer to a 4-year university for the final 2 years of college. Also, you should try out for you school's basketball team this fall/winter :)

That sounds like a good plan. Double check with the city college to make sure it is free. You won't need the SAT if you're planning to transfer to UCSD. They will require you to have 60 credit hours and submit your college transcripts.

If that information isn't on the "transfer application" page of the UCSD website, you'll need to call the admissions office and ask.  Each university has it's own policy, but often universities will not as for an ACT or SAT score from transfer students.  This is because those tests indicate "potential college performance."  Transfer students have actual college performance instead. 

https://admissions.ucsd.edu/transfer/application-r...

https://admission.universityofcalifornia.edu/admis...

Call UCSD and find out. I transferred from a college to a Cal state college several years ago and don't recall having to take the SAT.

Most universities do not require an SAT or ACT score if you transfer with 60 or more credits pending. 

UCs do not require the SAT from transfer applicants. They do require that you complete all the general education and major preparation requirements prior to transfer. You don't need to complete them all by the time you apply, but you should be enrolled in the classes not yet completed (i.e. you can apply during your last semester of sophomore year to start as a junior). 

It's unlikely to be accepted to a UC as a transfer student unless you are transferring from a California Community College.

Each university has its own entry requirements. You would need to UCSD what they require.

But usually if you already have college credits, they will look at those, your GPA, etc from those classes over an SAT score. The SAT can "maybe" guess what you will do in the college. The classes you have already taken prove what you cam do in college. So most schools do not require an SAT for a transfer.