Let $G$ be a (connected) reductive group over some ground field $F$ and $G^*$ its unique quasi-split inner form. Denote by $\operatorname{rank}_F G$ the split rank of $G$ and likewise for $G^*$. Is it true that 

$$\operatorname{rank}_F G\le \operatorname{rank}_FG^*$$ 

with equality holds only if $G$ is isomorphic to $G^*$? I am mostly wondering about the case when $F$ is a non-archimedean local field, but any suggestion/reference will be great. Thanks!