For hydrochloric acid (HCl), a strong acid, complete dissociation in water means the concentration of \( \text{H}^+ \) ions equals the acid's concentration, which is 0.01 M. The pH calculation formula is:
\[
\text{pH} = -\log [\text{H}^+]
\]
Substituting \( [\text{H}^+] = 0.01 \) M yields:
\[
\text{pH} = -\log (0.01) = 2
\]
Therefore, the solution's pH is 2, corresponding to option (2).