There is no US Federal marriage registry, nor (to the best of my knowledge) are there any state-level ones for marriages which did not take place in that state.
There is no requirement for you to 'register' a foreign marriage in the USA, and it's simply not possible to do so since there is no register of local marriages either outside of the state where the marriage took place.
The only thing you might want to do, particularly if your foreign marriage certificate is not in English, is to get a translation and/or apostille (neither of which requires your presence in the USA).
If you're in the USA and need to prove that you're married, you show your marriage certificate (and possibly the translation and/or apostille).