So, I'm building a website, but I don't want to use full bitcoin core. Is there any SPV wallet with RPC interface, so I can accept payments using it?
if you just want to receive bitcoins then you don't need a wallet on the server. you can install a deterministic wallet like electrum or mycelium on your own device. then on the server you just need a library that will take your wallet's extended public key and generate addresses from that. this way there is no risk of theft since the private keys remain on your own device and not on the server.
if you tell us what programming language you are using for your web application we can suggest some libraries.