Absent any document to the contrary, a transfer of property from a parent to a child will be presumed to be a gift. And, under Cal. Civil Code
1146-1148, a gift is irrevocable except in view of impending death. So, unless your father was dying at the time he gave you the money, then I doubt that he could come up with a set of facts that would permit him to successfully sue.
However, as a matter of law, your father could claim that there was an agreement for repayment, and then it would be his burden to prove that agreement. So, the answer is that your father can sue -- but he probably can't win.
Concerning an indemnity agreement, what you're talking about is a "release." That is, something like: "In consideration for the payment of $____, father agrees to irrevocably and fully release son from any liability for any debt owed by son to father, if said debt arose prior to the date of signing of this agreement by father."
There are dozens of free release documents floating around the internet, and some relatively inexpensive documents. That said, I don't think your dad has a case -- but he can sue, so if you think a release would let you sleep at night, then maybe it's a good idea.
Hope this helps.