Ask DMV.  That's certainly not old enough for the "HORSELESS CARRIAGE"
plates, but those aren't the only special series of plates for older
cars in CA.

I don't think California has any concept of special plates for an
antique car or horseless carriage or whatever for regular driving.

They do offer both "antique" (post-1922 but >25 years old and of
"historical interest"; not clear who judges that or under what
criteria) and "horseless carriage" (pre-1923, or pre-1965 with 16 or
more cylinders) plates.  However, as I understand it, those put your
car into some kind of show/ club-event/ parade classification; as long
as you hold them you are not supposed to use the car for ordinary
street driving, and if you want to recommission the vehicle for normal
use you have to surrender those plates and get the regular sort.

I think antique (1942 or earlier) *motorcycles* may be granted special
plates for regular use, but not cars.

Of course,  many a "survivor" that has always been in California still
bears its older-style style plates, but that's a different matter --
they were the regular issue plates back when it was new.

See for instance
http://www.dmv.ca.gov/pubs/plates/specialplates.htm
and
http://www.dmv.ca.gov/forms/reg/reg17a.pdf

Cheers,
--Joe