The warrant is for Thawatchai Promchan, according to the police spokesmen Facebook page.
Mr Thawatchai, 42, is a native of Prachinburi's Prachantakham district.
He will be charged with owning and carrying a gun and ammunition in public without permission and with firing a gun in public without reasonable cause.
Phra Khanong Provincial Court earlier issued an arrest warrant for another man suspected to be involved in Sutin's killing using a sketch based on images captured on CCTV. The suspect is yet to be identified.
Sutin was shot dead on Jan 26. He had led a group of People's Democratic Reform Committee (PDRC) protesters to block advance voting near Wat Sri Iam in Bang Na. The group were leaving the area on a truck when the attack occurred.
Porntip Rojanasunan, former director-general of the Central Institute of Forensic Science, conducted an autopsy on Sutin. She said Sutin was shot twice in his right side. One bullet hit his right armpit and exited on the left side of his back. The other hit the right side of his neck and exited above his left ear.