He Swore Not to do Something,
Then He Was Forced to do it

Question :

I swore upon a copy of the Qur'an that I would not do a certain thing, but circumstances compelled me to violate this oath and I want to atone for this sin, so what is the way to do that?

Answer:

You must make atonement for an unfulfilled oath if did not abandon the thing which you swore to abandon, whether you swore on a copy of the Qur'an or not, according to the Words of Allah, the Almighty, Most High:
"Allah will not punish you for what is unintentional in your oaths, but He will punish you for your deliberate oaths; for its expiation (a deliberate oath) feed ten Masäkin (poor persons), on a scale of the average of that with which you feed your oven families, or clothe them or manumit a slave. But whosoever cannot afford (that), then he should fast for three days. That is the expiation for the oaths when you have sworn. And protect your paths (i.e., do not swear much).

If you fed ten poor people lunch or dinner or clothed them, you would have fulfilled the atonement thereby. If you gave each one of them half a Sa' of dates, wheat or rice, it would be enough for you.

If the thing you swore about was an act of disobedience to Allah such as smoking or drinking intoxicants or the like it would be forbidden for you to do it, even if you had not sworn to abandon it. So fear Allah and avoid what Allah has forbidden to you.

Source:
Ibn Baz
Fatawa Islamiyah, Vol. 6 Pages 379-380