Narrated `Abdullah bin Zaid: Allah'sMessenger (ﷺ) went out to this Musalla (praying place) to offer the prayer of Istisqa.' He invoked Allah for rain and then faced the Qibla and turned his Rida' (upper garment) inside out. Sahih al-Bukhari Vol.8: 6343 
Once you have entered Masjid ul Haram make Al Idtibaa’ (عابطضلاا), which is to uncover the right shoulder and cover the left with the ridaa’ (upper towel). When you have completed your seventh Tawaf, cover right shoulder with the ridaa’ (towel).