The notion of rectifying curve in the Euclidean space is introduced by Chen as a curve whose position vector always lies in its rectifying plane spanned by the tangent and the binormal vector field t and $n_2$ of the curve, [1]. In this study, we have obtained some characterizations of semi-real spatial quaternionic rectifying curves in $mathbb{R}^3_1$. Moreover, by the aid of these characterizations, we have investigated semi real quaternionic rectifying curves in semi-quaternionic space $mathbb{Q}_v$.