  Starting from the $\kappa$-distribution function, obtained by applying the
maximal entropy principle to the $\kappa$-entropy [G. Kaniadakis, Phys. Rev. E
66 (2002), 056125], we derive the expression of the canonical
$\kappa$-partition function and discuss its main properties. It is shown that
all important macroscopical quantities of the system can be expressed employing
only the $\kappa$-partition function. The relationship between the associated
$\kappa$-free energy and the $\kappa$-entropy is also discussed.
