  Detailed information of the low-energy interaction between the charmonia
({\eta}c and J/{\psi}) and the nucleon is indispensable for exploring the
formation of charmonium bound to nuclei. In order to investigate the
charmonium-nucleon interactions at low energies, we adopt two essentially
different approaches in lattice QCD simulations. The charmonium-nucleon
potential can be calculated from the equal-time Bethe-Salpeter amplitude
through the effective Schr\"odinger equation. This novel method is based on the
same idea originally applied for the nucleon force by Aoki- Hatsuda-Ishii.
Another approach is to utilize extended L\"uscher's formula with partially
twisted boundary conditions, which allows us to calculate the s-wave phase
shift at any small value of the relative momentum even in a finite box. We then
extract model independent information of the scattering length and the
effective range from the phase shift through the effective-range expansion. Our
simulations are carried out at a lattice cutoff of $1/a \approx$ 2 GeV in a
spatial volume of (3 fm)^3 with the non-perturbatively O(a)-improved Wilson
fermions for the light quarks and a relativistic heavy quark action for the
charm quark. Although our main results are calculated in quenched lattice
calculations, we also present a preliminary full QCD result by using the 2+1
flavor gauge configurations generated by PACS-CS Collaboration. We have found
that the charmonium-nucleon potential is weakly attractive at short distances
and exponentially screened at large distances. We have also successfully
evaluated both the scattering length and effective range from the
charmonium-nucleon scattering phase shift.
