Iridates are of current great interest for their entangled spin-orbital state and possibly exotic properties. In this work, using density functional calculations, we have demonstrated that the hexagonal spin-chain materials Sr3MIrO6 (M = Ni, Co) are an iridate system in which the spin-orbit coupling (SOC) tunes the magnetic and electronic properties. The significant SOC alters the orbital state, the exchange pathway, and thus the magnetic structure. This work clarifies the nature and the origin of the intra-chain antiferromagnetism of Sr3MIrO6 and well accounts for the most recent experiments.