  Let $(H_{\mathbf{R}}, U_t)$ be any strongly continuous orthogonal
representation of $\mathbf{R}$ on a real (separable) Hilbert space
$H_{\mathbf{R}}$. For any $q\in (-1,1)$, we denote by
$\Gamma_q(H_{\mathbf{R}},U_t)^{\prime\prime}$ the $q$-deformed Araki-Woods
algebra introduced by Shlyakhtenko and Hiai. In this paper, we prove that
$\Gamma_q(H_{\mathbf{R}},U_t)^{\prime\prime}$ has trivial bicentralizer if it
is a type $\rm III_1$ factor. In particular, we obtain that
$\Gamma_q(H_{\mathbf{R}},U_t)^{\prime\prime}$ always admits a maximal abelian
subalgebra that is the range of a faithful normal conditional expectation.
Moreover, using Sniady's work, we derive that
$\Gamma_q(H_{\mathbf{R}},U_t)^{\prime\prime}$ is a full factor provided that
the weakly mixing part of $(H_{\mathbf{R}}, U_t)$ is nonzero.
