Is there any expiation for having intercourse with a woman in her back passage?

Firstly: 

It is haram to have intercourse with one’s wife in her back passage, and the Prophet (peace and blessings of Allah be upon him) said that the one who does that is cursed. 

We have quoted the evidence from the Quran and Sunnah to show that it is haram, as well as describing some of the evil consequences of that, in the answer to question no. 1103 and 6792. 

Islam has not stipulated any expiation for this action, so there is no expiation for it apart from repentance and regret, and turning back to Allah. 

Shaykh Ibn Baaz (may Allah have mercy on him) was asked: What is the ruling on having intercourse with a woman in her back passage? Is there any expiation required of the one who does that?  

He replied: 

Having intercourse with a woman in her back passage is a major sin and is one of the most heinous acts of disobedience, because it was narrated that the Prophet (peace and blessings of Allah be upon him) said: “Cursed is the one who has intercourse with his wife in her back passage.” Narrated by Abu Dawood, 2162; classed as hasan by al-Albaani in Saheeh Abi Dawood. 

And he (peace and blessings of Allah be upon him) said: “Allah will not look at a man who had intercourse with a man or a woman in the back passage.” Narrated by al-Tirmidhi, 1166; classed as hasan by al-Albaani in Saheeh al-Tirmidhi. 

What the one who has done that must do is hasten to repent sincerely, which means giving up the sin and abstaining from it out of respect for Allah and out of fear of His punishment, regretting what he has done of that and sincerely resolving never to go back to it, as well as striving to do righteous deeds. Whoever repents sincerely, Allah will accept his repentance and forgive his sins, as Allah says (interpretation of the meaning): 

“And verily, I am indeed forgiving to him who repents, believes (in My Oneness, and associates none in worship with Me) and does righteous good deeds, and then remains constant in doing them (till his death)”

[Ta-Ha 20:82]

“And those who invoke not any other ilaah (god) along with Allah, nor kill such person as Allah has forbidden, except for just cause, nor commit illegal sexual intercourse and whoever does this shall receive the punishment.

69. The torment will be doubled to him on the Day of Resurrection, and he will abide therein in disgrace;

70. Except those who repent and believe (in Islamic Monotheism), and do righteous deeds; for those, Allah will change their sins into good deeds, and Allah is Oft‑Forgiving, Most Merciful”

[al-Furqaan 25:68-70] 

There is no expiation required of one who has anal intercourse, according to the more correct of the two scholarly opinions, and his wife does not become haram to him because of that, rather she remains his wife. But she does not have to obey him in this grave evil; rather she is obliged to refuse, and to demand a annulment of her marriage to him if he does not repent. We ask Allah to keep us safe and sound from that. 

From Fataawa Islamiyyah, 3/256 

Al-Bayhaqi (may Allah have mercy on him) said: 

If he does that (i.e., has intercourse with her in the back passage), then he should be punished (i.e., the judge or ruler should mete out a punishment that will deter him and others like him), because he has committed a sin for which there is no stipulated hadd punishment or expiation. 

Kashshaaf al-Qinaa’, 5/190 

So he clearly stated that it is a sin, but no expiation is required. 

See Ansa al-Mataalib, 4/162; Mughni al-Muhtaaj, 5/624 

Secondly: 

Many people make the mistake of thinking that because there is no expiation stipulated for a particular sin that it is an insignificant matter and is a minor sin. This way of thinking is not correct. Rather if one were to say that Allah has not stipulated any expiation for anal intercourse because it is too serious to be expiated by any expiation, that would not be farfetched. As Imam Maalik says concerning swearing a false oath (al-yameen al-ghamoos): it is too serious to be expiated by any expiation. 

Al-Taaj wa’l-Ikleel, 4/406; see also al-Mudawwanah, 1/577 

And Allah knows best.