CA VC Sec. 12502 says this:
12502 (a) The following persons may operate a motor vehicle in this
state without obtaining a driver’s license under this code:
(1) A nonresident over the age of 18 years having in his or her
immediate possession a valid driver’s license issued by a foreign
jurisdiction of which he or she is a resident, except as provided in
Sec. 12505 says, among other things, this:
c) Any person entitled to an exemption under Section 12502, 12503, or
12504 may operate a motor vehicle in this state for not to exceed 10
days from the date he or she establishes residence in this state,
eexcept that ( )1 a person shall not operate a motor vehicle for
employment in this state after establishing residency without first
obtaining a license from the department.
( )3 (f) Subject to Section 12504, a person over the age of 16 years
who is a resident of a foreign jurisdiction ( )4 may operate a motor
vehicle in this state without obtaining a license from the department,
( )5 unless the department determines that the foreign jurisdiction
does not meet the licensing standards imposed by this code.
It also defines the term "resident" in 12505(a) (you can read through the link). As a J1 student you're probably not falling under any of the categories making you resident in California.
So basically, if your foreign license adequately identifies you (in English) and identifies the classes of vehicles you may drive - you can use it in California during your visit. Unless of course the DMV explicitly exclude Indian licenses (as they are allowed per 12505(f)), but I have not found any evidence of such exclusion.