You can push the full URL to a prop (it has a 100 char limit) or an eVar (it has a 255 char limit) for a full URL value. Note the character limits I mentioned, as your URL values may get truncated.
But for tracking query string parameters, it is usually better to track those values in separate props or eVars. It makes it easier to filter or break things down this way. You also decrease your chances of reaching unique value limits in your reports. You also better ensure you get the full URL parameter values vs. them potentially truncating from full URL values.