  We study ionization of aligned H$_2^+$ in strong elliptically-polarized laser
fields numerically and analytically. The calculated offset angle in
photoelectron momentum distribution is several degrees larger for the molecule
than a model atom with similar ionization potential at diverse laser
parameters. Using a strong-field model that considers the properties of
multi-center and single-center Coulomb potentials, we are able to
quantitatively reproduce this angle difference between the molecule and the
atom. Further analyses based on this model show that the response time of
electron to light which is encoded in the offset angle and is manifested as the
time spent in tunneling ionization, is about 15 attoseconds longer for the
molecule than the atom. This time difference is further enlarged when
increasing the internuclear distance of the molecule.
