If in anger a husband takes upon himself a promise not to touch his wife what should he do when he is now repenting?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions. 

Whoever takes an oath that he will not touch his wife and regrets afterwards can touch his wife provided he pays the expiation of breaking the oath.  The Prophet (Sallallahu Alaihi wa Sallam) said: "Whoever makes an oath and then sees that something else would be better than it, should do Kaffarah (expiation) for his oath and do that which is better." [Reported by Imam Muslim]

The expiation is as mentioned in the verse: {…for its expiation (a deliberate oath) feed ten Masâkin (poor persons), on a scale of the average of that with which you feed your own 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 oaths (i.e. do not swear much)….}[5:89].

One may choose one of the three kinds of expiations mentioned in the verse, i.e. (feeding, clothing and freeing a slave).  If one cannot do one of them one has to fast for three days. 

The above details apply to the one who does not take an oath of divorce.  If he takes an oath of divorce the divorce is effective.  But he may sleep with his wife if he had not delivered two divorces previously.  However, if one wants to take his wife back after delivering first divorce it is better to make that intention before having sex.  If he had divorced her twice before this oath then the preponderant opinion is that he cannot sleep with her, due to this oath since the divorce becomes effective by merely inserting his penis into her vagina.

All the above rulings apply if one abstains from his wife for four months or less.  After four months a woman has the right to demand her sexual rights.  In this case a husband is obliged to answer her call and has to break his oath by paying expiation or divorcing her.

Allah knows best.