Yes, but it would require some work.
You will need to override/replace the standard authentication module that ships with .NET and replicate all the existing functionality with the exception of calls to the RSA Encrypt/Decrypt methods you want to use instead.
See http://msdn.microsoft.com/en-us/library/system.web.security.formsauthentication.encrypt.aspx
You will also need to edit all the standard builtin login pages if you are using those.
As a template, inspect the source for the FormsAuthenticationTicket and you will see how the string is constructed that contains parameters such as UserID, Expiry Date etc, and then pass that string into the Encrypt method, which in turn is then used as the cookie value.
Your new auth module will then have to reverse that encryption and validate the user as before.
It's a fair amount of work for relatively little gain, depends on how badly you want to use RSA over the standard encryption methods used (they already offer some powerful encruyption methods right out the box see http://www.sourcetree.net/sourcetree/Development/Aspnet%20Examples/GenerateMachineKeyForWebConfig.aspx)