Sylhet Metropolitan Magistrate Anwarul Haque granted the remand on Friday.
He also gave police seven more days to quiz accused Muhit Alam and Ismail Hossain Ablus. Their five-day remand ended on Friday.
Locals caught Ali from Sheikhparha earlier in the day and turned him over to police.
Investigator Detective Branch Inspector Suranjit Tarafder said he appealed for 10 days.
On Jul 8, locals caught Muhit when he was trying to dump the body of Rajan after brutally beating him to death with others.
The torturers filmed the brutality and posted on Facebook, igniting uproar.
One of the accused, Kamrul Islam, fled to Saudi Arabia, but caught in Jeddah.
Nur Mia, who allegedly captured the torture on mobile phone, was arrested on Thursday.