There is not a free cloud CxSAST instance available as Checkmarx is a paid product, so ask your employer to look into purchasing an instance or, if you are the employer, you can evaluate an instance.
However if you are a partner submitting for the appexchange security review, you can use the cloud service. Salesforce has purchased a license which grants you one free scan for each package version id, when scans are on a per-package basis. https://security.secure.force.com/sourcescanner/
There is also a customer portal which has line of code restrictions, 30K/month with a 12 month lookback, or (equivalently) 360K/year.
Unfortunately having the partner portal expose an API that would allow you to hook your IDE into the partner portal is not on the table, as you need to login with your partner account, we do not expose the checkmarx instances directly to the public (just imagine the load balancing or security concerns with giving every partner an account), there is custom pre and post processing happening between the job request and the result (you may have noticed the scan result html files you retrieve from the portal look nothing like the checkmarx reports) and there would be no way to associate the code you are scanning to a package version in order to enforce licensing restrictions. For the customer scanner, the line of code restrictions would not allow the plugin to be usable.