  For the first time, we experimentally determine the infrared magic wavelength
for the $^{40}$Ca$^{+}$ $4s\, ^{2}\!S_{1/2} \rightarrow 3d\,^{2}\!D_{5/2}$
electric quadrupole transition by observation of the light shift canceling in
$^{40}$Ca$^{+}$ optical clock. A "magic" magnetic field direction is chosen to
make the magic wavelength insensitive to both the linear polarization purity
and the polarization direction of the laser. The determined magic wavelength
for this transition is 1056.37(9)~nm, which is not only in good agreement with
theoretical predictions but also more precise by a factor of about 300. Using
this measured magic wavelength we also derive the differential static
polarizability to be $-44.32(32)$~a.u., which will be an important input for
the evaluation of the blackbody radiation shift at room temperatures. Our work
paves a way for all-optical-trapping of $^{40}$Ca$^{+}$ optical clock.
