  The repeating fast radio burst (FRB) source that produced FRB 121102 was
recently localized in a star forming galaxy at $z=0.193$, which is associated
with an extended radio source at the burst location. One possibility is that
the repeating FRBs are produced by a new-born magnetar, which also powers the
radio nebula. If so, the magnetar may produce $\gamma$-ray emission due to
magnetic dipolar spin-down. The luminosity depends on the magnetar spin
parameters and age. We process the eight-year Fermi LAT data at the position of
FRB 121102 and place an energy flux upper limit of $\sim 10^{-11} \ {\rm erg \
cm^{-2} \ s^{-1}}$ in time bins with six-month intervals, and an accumulated
energy flux upper limit of $\sim 4\times 10^{-12} \ {\rm erg \ cm^{-2} \
s^{-1}}$ over the eight year span. The corresponding $\gamma$-ray luminosity
upper limits are $\sim 10^{45} \ {\rm erg \ s^{-1}}$ and $\sim 4\times 10^{44}
\ {\rm erg \ s^{-1}}$ for the time-resolved and time-integrated analyses,
respectively. We discuss the implications of these limits on the young magnetar
model.
