At the cut-off frequency, when $\omega = \omega_c$:
$|H|= {1 \over \sqrt{1+ (\omega_c RC)^2}} = \sqrt{1 \over 2}$
Therefore:
${1 \over {1+ (\omega_c RC)^2}} = {1 \over 2}
\\
1+(\omega_c RC)^2 = 2$
Thus the cut-off frequency is:
$$\omega_c = {1 \over {RC}}$$