If I commit a sin but then sincerely repent for it, can I take a false oath by the Quran to save my honour by denying that I committed that sin?
Bismihi ta'ala
Repenting from a sin is very important, and that's very good that you have sincerely repented from it, but it does not mean you are able to deny having committed it if confronted about it. Taking a false oath is a major sin, and worse than that is swearing a false oath on the holy Quran.
As for saving your honour, you need to weigh out what the situation is, and what kind of consequences there will be for revealing this sin, or whether there will be detremental damage to you, or harm.
It might be advisable that you somehow change the scenario, or do tawriyah, to avoid severe backlash, if that is what the situation will be.
With prayers for your success.