  We study rigidly rotating strings in the $\varkappa$-deformed $AdS_3 \times
S^3$ background. We find out two classes of solutions corresponding to the
giant magnon and single spike solutions of the string rotating in two
$S^2_{\varkappa}$ subspace of rotations reduced along two different isometries.
We verify that the dispersion relations reduce to the well known relation in
the $\varkappa\rightarrow 0$ limit. We further study some oscillating string
solutions in the $S^3_{\varkappa}$ subspace.
