Hydrochloric acid (HCl), a strong acid, completely dissociates in water according to the equation:
\[
\text{HCl} \rightarrow \text{H}^+ + \text{Cl}^-
\]
Consequently, the concentration of hydrogen ions, denoted as $[\text{H}^+]$, is equivalent to the HCl concentration, which is 0.01 M.
The pH is determined by the formula:
\[
\text{pH} = -\log [\text{H}^+]
\]
Upon substitution of the value:
\[
\text{pH} = -\log (0.01) = 2
\]
Therefore, the solution exhibits a pH of 2.