Yes, oiling hair is part of the Sunnah, particularly on Fridays.
According to Al-Bukhari, the Prophet Muhammad (Sallallahu Alayhi Wassalam) said, "Whoever takes a bath on Friday, purifies himself as much as he can, then uses his (hair) oil or perfumes himself with the scent of his house, then proceeds (for the Jumua prayer) and does..." This indicates that applying oil to the hair is a recommended practice on Fridays, aligning with the Sunnah.
