Hello Anastasiys
Cisco’s official advice on this issue is to never use self-signed certificates to authenticate. This kind of defeats the purpose of the security that the whole CA and certificates infrastructure delivers.
It is possible to apply self-signed certificates on a site-to-site VPN configuration on Cisco IOS devices, however, I’m not so sure about ASAs. You can do it for ANyconnect connections, but for site to site using ASAs, some users seem to indicate that it cannot be done.
If you want to implement a site-to-site VPN without a CA, your best bet is to simply use IKEv2 IPSEC.
I hope this has been helpful!
Laz