Other than a VPN, you can also try using a proxy and using a software called proxifier, that would redirect all your incoming/outgoing traffic from your computer. Please note that there may be a little bit more configuration for RDP on that respective software, as you may need to do some software binding to a specific IP.
That software also allows you to use SOCKS connectivity, and given the simple and basic nature of SOCKS (which is a much simpler protocol as compared to HTTP/HTTPS), this would double up on your anonymity when logging into the VPS, as the risk of getting your computer's IP being logged would also be lesser.