  Recent accurate measurements of cosmic-ray (CR) species by ATIC-2, CREAM, and
PAMELA reveal an unexpected hardening in the proton and He spectra above a few
hundred GeV, a gradual softening of the spectra just below a few hundred GeV,
and a harder spectrum of He compared to that of protons. These newly-discovered
features may offer a clue to the origin of high-energy CRs. We use the ${\it
Fermi}$ Large Area Telescope observations of the $\gamma$-ray emission from the
Earth's limb for an indirect measurement of the local spectrum of CR protons in
the energy range $\sim 90~$GeV-$6~$TeV (derived from a photon energy range
$15~$GeV-$1~$TeV). Our analysis shows that single power law and broken power
law spectra fit the data equally well and yield a proton spectrum with index
$2.68 \pm 0.04$ and $2.61 \pm 0.08$ above $\sim 200~$GeV, respectively.
