The reorientation effect in Coulomb excitation with 62 MeV 35Cl projectiles was used to measure the static quadrupole moment of the first excited state in 24Mg. From a comparison of the inelastic scattering cross sections at CM scattering angles of 123.1° and 72.8°, a static quadrupole moment of Q = −0.243 ± 0.035 b was deduced. The E2 matrix element connecting the ground state and first excited state was also measured and corresponds to 20.3 ± 1.4 W.u. for the 2+ → 0+ transition. The results are compared with predictions of the rotational model.