It was the practice of the Prophet (peace and blessings be upon him):
"When he (peace and blessings be upon him) supplicated, he would turn the inner side of his palms towards his face."
Hadith Referenceصحیح الجامع الصغیر / حرف الكاف / 4721
Hadith Gradingالألبانی:صحيح
Hadith Takhrij[طب] عن ابن عباس. الضعيفة ٤١٩٩: طب - السائب بن خلاد. حم - خلاد بن السائب مرسلا.