Is there a student discount?

No student discount. But you can get a discount by purchasing zoo tickets at the Balboa Park visitor center. I believe it's 10% off.

Look online for prices.

I was once a student and boy, the discounts are not worth it. The rule of thumb is work, play, study. Pick two. Well i picked all three and snapped my crayons. I spent several weeks in a feral state near Arches National Park and was finally tranquilized by the warden. The zoo is great though, only four incidents occured within the park involving a frenzie of clawings. 5/5 will visit again.

Thanks but do you know how much it is?

I believe so.