Microscopic calculations of the l=0-5 phase-shifts for p+¹²C elastic scattering in the centre-of-mass incident energy range 0-18 MeV have been carried out using the single-channel resonating group method (RGM) and a purely central two-nucleon interaction. A complex generator coordinate technique has been used to evaluate the various matrix elements involved in the RGM calculations. For the ground state of the ¹²C nucleus a harmonic-oscillator shell-model wavefunction consisting of 19 Slater determinants which yields values of the RMS radius and charge form factor in good agreement with experiment has been used. Full antisymmetrisation has been performed in the calculation of all parts of the kernel functions except that corresponding to the Coulomb interaction. The calculated phase-shifts show the presence of sharp resonances for l=0 and 1 and a broad resonance for l=2. The differential cross sections for incident centre-of-mass energies of 1.75, 4.30, 8.86 and 14.95 MeV have also been calculated and are found to be in fair agreement with the experimental data.