The answer is no. But work is being done here AVM: EC math by jannotti · Pull Request #4924 · algorand/go-algorand · GitHub that will add the ability to perform pairing checks, which are necessary to verify groth16 type ZK-SNARKs. The type used in e.g. Tornado Cash:
You are proving that you know (from Algorand account B) of a path in a merkle tree to the root (that you have contributed to, but from Algorand account A) without actually revealing the path (as that would reveal that account B is linked to account A). A nullifier is also provided ensuring that someone can only make this proof of the particular path once.
Another way of describing it is proving that withdrawer account B is actually a member of the set of depositors (among which account A is included), without actually revealing which exact member.