A measurement of elastic deeply virtual Compton scattering γ*p→γp using e−p collision data recorded with the H1 detector at HERA is presented. The analysed data sample corresponds to an integrated luminosity of 145 pb−1. The cross section is measured as a function of the virtuality Q2 of the exchanged photon and the centre-of-mass energy W of the γ*p system in the kinematic domain 6.5<Q2<80 GeV2, 30<W<140 GeV and |t|<1 GeV2, where t denotes the squared momentum transfer at the proton vertex. The cross section is determined differentially in t for different Q2 and W values and exponential t-slope parameters are derived. The measurements are compared to a NLO QCD calculation based on generalised parton distributions. In the context of the dipole approach, the geometric scaling property of the DVCS cross section is studied for different values of t.