Yes, rationally connected varieties in characteristic zero are uniruled (a fact which follows essentially by definition).
One can think about this also by exploiting the following characterization of uniruled and rationally connected varieties, that can be found in Debarre's book Higher dimensional algebraic geometry, Chapter 4.
Let $X$ be a smooth projective variety of dimension $d$, defined over a field of characteristic zero. Recall that a rational curve $f \colon \mathbb{P}^1 \to X$ is called $r$-free if $f^*T_X \otimes \mathscr{O}_{\mathbb{P}^1}(-r)$ is generated by its global sections. By Grothendieck' s Theorem any vector bundle over $\mathbb{P}^1$ splits as a direct sum of line bundles, so $r$-free means $$f^*T_X = \mathscr{O}_{\mathbb{P}^1}(a_1) \oplus \ldots \oplus \mathscr{O}_{\mathbb{P}^1}(a_d),$$ with $a_i \geq r$ for every $i$. Now one has the following
Proposition. $X$ is uniruled if and only through a general point $x \in X$ there is a $0$-free rational curve. Moreover $X$ is rationally connected if and only if through a general point $x \in X$ there is a $1$-free rational curve.