Is there a non surgical procedure for anal fistula?

Not really: There are some fistula plugs that can be used, and while it is technically "surgery", it can be way less invasive because the fistula tract is scraped, then the plug inserted. There's also something called a Seton that can be used for a while, that helps in some situations. See a colorectal surgeon for a proper evaluation and ask about these things. Hope this helps!