All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
We do not know any specific supplication for the ‘Aqeeqah but it is permissible when slaughtering it to say Bismillaah and Allaahu Akbar [in the Name of Allaah and Allaah is the Greatest] and then one should say the name of the person for whom the ‘Aqeeqah is slaughtered.
Shaykh Ibn ‘Uthaymeen said about what is permissible to do or say when slaughtering: “After saying Bismillaah and Allaahu Akbar, one should say the name of the person for whom he is slaughtering the ‘Aqeeqah or the sacrifice, and then he should ask Allaah to accept it from him saying: “Bismillaah Wa Allaahu Akbar, O Allaah this is from You and for You on my behalf (if it is for him), or on behalf of so and so (if it is for someone else). O Allaah accept from me (if it for him), or O Allaah accept it from so and so (if it is for someone else).” [End of quote]
Hence, you should know that the one who says the mention of Allaah is the one who carries out the slaughtering whether he is the one who is obligated to offer the ‘Aqeeqah or he is doing it on behalf of someone else.
For more benefit on the most important rulings on ‘Aqeeqah, please refer to Fataawa 83120 and 81462.
Allaah Knows best.