  Measurements of temperature-dependent in-plane resistivity, $\rho(T)$, were
used to determine the upper critical field and its anisotropy in high quality
single crystals of stoichiometric iron arsenide superconductor KFe$_2$As$_2$.
The crystals were characterized by residual resistivity ratio,
$\rho(300K)/\rho(0)$ up to 3000 and resistive transition midpoint temperature,
$T_c$=3.8 K, significantly higher than in previous studies on the same
material. We find increased $H_{c2}(T)$ for both directions of the magnetic
field, which scale with the increased $T_c$. This unusual linear $H_{c2}(T_c)$
scaling is not expected for orbital limiting mechanism of the upper critical
field in clean materials.
