Yes, since your J-1 doesn’t have the two-year home residency rule, you can marry your U.S. citizen partner and adjust your status from inside the U.S. You’ll file both Form I-130 and I-485 together. You don’t have to leave. Just make sure you stay in the U.S. legally until you apply.

You can stay and adjust status, but make sure you don’t overstay without filing. Once your J-1 program ends, you don’t have status unless you take action. It’s safest to get married and file before your grace period ends, so your presence stays lawful. A lawyer can help you file everything correctly.