There is nothing wrong with putting oil on the hair during the day in Ramadaan

There is nothing wrong with putting oil on the hair during
the day in Ramadaan and that does not affect the fast. 

Shaykh Ibn Baaz (15/259) was asked: what is the ruling on
using kohl and cosmetics for women during the day in Ramadaan? Does that
break the fast or not? 

He replied: 

Kohl does not break the fast for women or for men, according
to the more correct of the two scholarly opinions, but it is better to use
it at night for one who is fasting. The same applies to things that are used
to beautify the face such as soap and creams etc, that are applied
externally to the skin, such as henna, make-up and the like. There is
nothing wrong with the fasting person using them, but make-up should not be
used if it is harmful to the face. 

Shaykh Ibn ‘Uthaymeen said in Fataawa al-Siyaam
(228): 

All kinds of creams,
whether used on the face, back or elsewhere, have no effect on the fasting
person and do not break his fast. 

The Standing Committee (10/253) was asked: Does kohl or cream
used by a woman during the day in Ramadaan break the fast or not? They
replied: 

Whoever uses kohl during the day in Ramadaan when fasting
does not invalidate his or her fast. The same applies to one who puts oil on
the hair during the day in Ramadaan – it does not break the fast.”.