We present a dispersive representation of the D-term form factor for hard exclusive reactions, using unsubtracted t-channel dispersion relations. The t-channel unitarity relation is saturated with the contribution of two-pion intermediate states, using the two-pion distributions amplitude for the γ⁎γ→ππ subprocess and reconstructing the ππ→NN¯ subprocess from available information on pion-nucleon partial-wave helicity amplitudes. Results for the D-term form factor as function of t as well as at t=0 are discussed in comparison with available model predictions and phenomenological parametrizations. Keywords: Dispersion relations, Deeply virtual Compton scattering, Generalized parton distributions