The phase shift of the filter is ($\phi = {\phi_o - \phi_i}$): $${\phi = tan^{-1} \left({0 \over 1} \right) - tan^{-1} \left({{\omega RC} \over 1} \right)} \\= -tan^{-1} \left(\omega RC \right)$$ Hence the gain and phase shift of a Passive Low-Pass filter are:
$|H|={1 \over {\sqrt{1+(\omega RC)^2}}} \\ \phi = -tan^{-1} (\omega RC)$