You can fix your RNG seed with the flags:
-constant_seed
-jran #######
Where ### is your seed number. (-constant_seed alone gets you a seed of 1111111). Your seed should be reported at the top of each log file. Fixing the RNG seed ensures the random number generator takes an identical trajectory.
Notice that changing parameters for the simulation will necessarily drive you down a different Monte Carlo path – the RNG trajectory will be unchanged, but Monte Carlo will make different accept/reject choices because you will have different scores due to the new parameters. There is no way to ask Rosetta to, say, “always make exactly the same rotamer substitutions” if you have changed other parts of scoring, etc., so it might not be possible to do just what you want. Which parameters are you changing?