Shaving the head is preferrable to cutting the hair, although cutting the hair is permissible Sahih Muslim 1301 b
Arabic hadith text
وَحَدَّثَنَا يَحْيَى بْنُ يَحْيَى، قَالَ قَرَأْتُ عَلَى مَالِكٍ عَنْ نَافِعٍ، عَنْ عَبْدِ اللَّهِ بْنِ عُمَرَ، أَنَّ رَسُولَ اللَّهِ صلى الله عليه وسلم قَالَ "اللَّهُمَّ ارْحَمِ الْمُحَلِّقِينَ " . قَالُوا وَالْمُقَصِّرِينَ يَا رَسُولَ اللَّهِ قَالَ " اللَّهُمَّ ارْحَمِ الْمُحَلِّقِينَ " . قَالُوا وَالْمُقَصِّرِينَ يَا رَسُولَ اللَّهِ قَالَ " وَالْمُقَصِّرِينَ "
Translation
Abdullah b. Umar (Allah be pleased with him) reported Allah's Messenger (ﷺ) as having observed
O Allah, have mercy upon those who get their heads shaved. They (the Companions) said: Messenger of Allah, (what about those) who have got their hair clipped? He said: O Allah, have mercy upon those who have got their heads shaved. They (again) said: Allah's Messenger, (what about those) who have got their hair clipped? Thereupon he said: (O Allah, have mercy upon those) who have got their hair clipped.