Rahima’Ullah means Allah have mercy upon him or May Allah have Mercy on Him. It is a phrase often used after mentioning any Islamic personality who came after the companions of Prophet Muhammad (May Allah honour Him and grant Him peace). The word Rahima’Ullah used in abbreviations with short form as RA or ra.
Rahima’Ullah- رحمه الله
Rahima’Ullah is a dua used for Pious Muslims who died. Therefore any Muslim who has done good things for Islam, after his death can be referred as Rahima’Ullah meaning May Allah Mercy upon him. 
Allah سبحانه و تعالى has set the criteria for a pious person in the Qur’an. Allah سبحانه و تعالى says: O mankind, indeed We have created you from male and female and made you peoples and tribes that you may know one another. Indeed, the most noble of you in the sight of Allah is the most righteous of you. Indeed, Allah is Knowing and Acquainted. Qur’an.Surah Hujrath 49:13