The anisotropic superconducting properties of single crystals of Cu0.07TiSe2 were studied by measurements of magnetization and electrical resistivity. TC is around 3.9 K, and the measured upper critical field (Hc2) values are ~1.25 T and 0.8 T, for applied field parallel and perpendicular to the TiSe2 planes, respectively. The anisotropy ratio gamma_anis = H^ab_c2 / H^c_c2 is close to 1.6 and nearly temperature independent. The lower critical field (Hc1) values are much smaller (~ 32 Oe for H||ab and 17 Oe for H||c); demagnetizing corrections for field perpendicular to the thin plate crystals are required for the determination of H^c_c1. The anisotropy of the critical fields is described well by the anisotropic Ginzburg-Landau (GL) theory, and the characteristic GL parameters are determined and discussed.