We propose a method for the lattice QCD computation of nucleon–nucleon low-energy interactions. It consists in simulating QCD in the background of a “electromagnetic” field whose potential is non-vanishing, but whose field strength is zero. By tuning the background field, phase-shifts at any (but small) momenta can be determined by measuring the shift of the ground state energy. Lattice sizes as small as 5 Fermi can be sufficient for the calculation of phase shifts up to momenta of order of mπ/2.