  TaSe$_2$ has several different polytypes and abundant physical properties
such as superconductivity and charge density waves (CDW), which had been
investigated in the past few decades. However, there is no report on the
physical properties of 4$Ha$ polytype up to now. Here we report the crystal
growth and discovery of superconductivity in the tantalum self-intercalated
4$Ha$-Ta$_{1.03}$Se$_2$ single crystal with a superconducting transition onset
temperature $T_{\rm c}$ $\approx$ 2.7 K, which is the first observation of
superconductivity in 4$Ha$ polytype of TaSe$_2$. A slightly suppressed CDW
transition is found around 106 K. A large $\mu_0H_{\rm c2}/T_{\rm c}$ value of
about 4.48 is found when magnetic field is applied in the $ab$ plane, which
probably results from the enhanced spin-orbit coupling(SOC). Special stacking
faults are observed, which further enhance the anisotropy. Although the density
of states at the Fermi level is lower than that of other polytypes, $T_{\rm c}$
remains the same, indicating the stack mode of 4$Ha$ polytype may be beneficial
to superconductivity in TaSe$_2$.
