  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 M\"ossbauer 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.
