  Let $G$ be a smooth connected linear algebraic group and $X$ be a $G$-torsor.
Totaro asked: if $X$ admits a zero-cycle of degree $d \geq 1$, then does $X$
have a closed \'etale point of degree dividing $d$? This question is entirely
unexplored in the literature for algebraic tori. We settle Totaro's question
affirmatively for algebraic tori of rank $\leq 2$.
