We report anisotropic dc magnetic susceptibility $chi(T)$, electrical resistivity $rho(T)$, and heat capacity $C(T)$ measurements on the single crystals of CaFe$_{2-x}$Co$_x$As$_2$ for $x$ = 0 and 0.06. Large sized single crystals were grown by the high temperature solution method with Sn as the solvent. For the pure compound with $x$ = 0, a high temperature transition at 170 K is observed which is attributed to a combined spin density wave (SDW) ordering and a structural phase transition. On the other hand, for the Co-doped samples for $x$ = 0.06, the SDW transition is suppressed while superconductivity is observed at $simeq$17 K. The superconducting transition has been confirmed from the magnetization and electrical resistivity studies. The $^{57}$Fe Mossbauer spectrum in CaFe$_2$As$_2$ indicates that the SDW ordering is incommensurate. In the Co-doped sample, a prominent paramagnetic line at 4.2 K is observed indicating a weakening of the SDW state.
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