  We present the first individual and stacking systematic search for
$\gamma$-ray emission in the GeV band with the {\it Fermi} Large Area Telescope
(LAT), in the directions of 45 super-luminous supernovae (SLSNe). No excess of
\gam rays from the SLSN positions was found. We report $\gamma$-ray luminosity
upper limits and discuss the implication of these results on the origin of
SLSNe in particular on the scenario of central compact object-aided SNe. From
the stacking search, we derive an upper limit at 95\% confidence level (CL) to
the $\gamma$-ray luminosity (above 600 MeV)
$L_{\gamma}<9.1\times10^{41}$\,erg\,s$^{-1}$ for an assumed $E^{-2}$ photon
spectrum, for our full SLSN sample. We conclude that the rate of the neutron
stars born with millisecond rotation periods {$P\lesssim 2\,$ms and
$B\sim10^{12-13}\,$G} must be lower than the rate of the observed SLSNe. The
luminosity limits obtained on individual sources are also constraining: in
particular, SN2013fc, CSS140222, SN2010kd, and PTF12dam can be born with
millisecond periods only if $B\lesssim 10^{13}\,$G.
