  We report the temperature dependencies of the upper critical fields
$H_{c\text{2}}^{\text{c}}(T)$ parallel to the c-axis and
$H_{c\text{2}}^{\text{ab}}(T)$ parallel to the ab-plane of single crystalline
CaKFe$_4$As$_4$ inferred from the measurements of the temperature-dependent
resistance in static magnetic fields up to 14 T and magnetoresistance in pulsed
fields up to 63 T. We show that the observed decrease of the anisotropy
parameter $\gamma(T)=H_{c\text{2}}^{\text{ab}}/H_{c\text{2}}^{\text{c}}$ from
$\simeq 2.5$ at $T_c$ to $\simeq 1.5$ at 25 K can be explained by interplay of
paramagnetic pairbreaking and orbital effects in a multiband theory of
$H_{c2}$. The slopes of $dH_{c\text{2}}^{\text{c}}/dT\simeq-4.4$ T/K and
$dH_{c\text{2}}^{\text{ab}}/dT \simeq-10.9$ T/K at $T_c$ yield an electron mass
anisotropy of $m_{ab}/m_c\simeq 1/6$ and short coherence lengths $\xi_c\simeq
5.8\,\text{\AA}$ and $\xi_{ab}\simeq 14.3\,\text{\AA}$. The behavior of
$H_{c\text{2}}(T)$ turns out to be similar to that of the optimal doped
(Ba,K)Fe$_2$As$_2$, with $H_{c\text{2}}^{\text{ab}}(0)$ extrapolating to
$\simeq 92$ T, well above the BCS paramagnetic limit.
