When it is said
It is the eleventh of the prayers before sleep in the Russian prayer book, said every night. Orthodox churches in America that use the Russian book say it too, in English.
Greek Orthodox Christians instead pray the older Greek prayer it was made from. The Russian book keeps that Greek prayer too, translated whole, among the morning prayers. So the Russian prayer book turns to the guardian angel twice a day, morning and night.
Where it comes from
No author known
Made in Kievan Rus’ from a Greek prayer
A scribe of Kievan Rus’ in the 1100s took the second half of an older Greek prayer to the guardian angel and reworked it. That is the judgment of Dalmat (Yudin), a Russian monk and scholar. The Greek prayer is printed among texts credited to St Macarius of Egypt, which the Orthodox Encyclopedia says are not his.
Hieromonk Dalmat (Yudin), Theological Herald 31, 2018 (in Russian); Orthodox Encyclopedia, Macarius the Great (in Russian)
A slip in the first copies
The first copies left out the main verb of one sentence, and each scribe filled it in his own way. Today’s “deliver me from all the cunning of the enemy” comes from the repair found in a Moscow copy of about 1370. The Greek had “keep me”.
Hieromonk Dalmat (Yudin), Theological Herald 31, 2018 (in Russian)
What the words mean
Why ask an angel to forgive?
The Greek prayer it was made from makes the sense plain. It asks the angel to forgive “all the ways I have grieved you”. So the angel is asked to forgive the grief our wrongs cause the one who guards us. The prayer of St John of Damascus says the same, that our sins anger “my holy guardian angel”.
Hieromonk Dalmat (Yudin), Theological Herald 31, 2018 (in Russian)
The Scripture in it
For He will command His angels concerning you to guard you in all your ways.
See that you do not look down on any of these little ones. For I tell you that their angels in heaven always see the face of My Father in heaven.
Are not the angels ministering spirits sent to serve those who will inherit salvation?
Bible text: Berean Standard Bible, public domain.
In Church Slavonic
Ангеле Христов, хранителю мой святый и покровителю души и тела моего, вся ми прости, елика согреших во днешний день, и от всякаго лукавствия противнаго ми врага избави мя, да ни в коемже гресе прогневаю Бога моего;
но моли за мя грешнаго и недостойнаго раба, яко да достойна мя покажеши благости и милости Всесвятыя Троицы и Матере Господа моего Иисуса Христа и всех святых. Аминь.
From the Russian prayer book, in modern Russian letters, on the Orthodox portal Azbyka.ru.