已知向量 $\boldsymbol{a}=(1, \sqrt{3}), \boldsymbol{b}=(\cos \theta, \sin \theta)$, 若 $\boldsymbol{a} / \boldsymbol{b}$, 则 $\tan \theta=(\quad)$ $\begin{array}{lll}\text {
$\because \boldsymbol{a}=(1, \sqrt{3}), \boldsymbol{b}=(\cos \theta, \sin \theta)$, 且 $\boldsymbol{a} / \boldsymbol{b}$,

$\therefore \sin \theta-\sqrt{3} \cos \theta=0, \quad \therefore \sin \theta=\sqrt{3} \cos \theta, \quad \therefore \tan \theta=\frac{\sin \theta}{\cos \theta}=\frac{\sqrt{3} \cos \theta}{\cos \theta}=\sqrt{3}$,

故选 B.