Yes, you can play Rust with a VPN. In fact, many Rust players use a VPN to protect their IP address, reduce the risk of DDoS attacks, and stay safer on public or shared networks.
Facepunch’s Terms of Service don’t explicitly prohibit using VPNs to play their games. That said, you should always use a VPN fairly and avoid using it to manipulate, exploit, or gain an unfair advantage in the game.