  We study loop corrections to scattering amplitudes in the world-volume theory
of a probe D3-brane, which is described by the supersymmetric Dirac-Born-Infeld
theory. We show that the D3-brane loop superamplitudes can be obtained from the
tree-level superamplitudes in the world-volume theory of a probe M5-brane (or
D5-brane). The M5-brane theory describes self-interactions of an abelian tensor
supermultiplet with $(2,0)$ supersymmetry, and the tree-level superamplitudes
are given by a twistor formula. We apply the construction to the
maximally-helicity-violating (MHV) amplitudes in the D3-brane theory at
one-loop order, which are purely rational terms (except for the four-point
amplitude). The results are further confirmed by generalised unitarity methods.
Through a supersymmetry reduction on the M5-brane tree-level superamplitudes,
we also construct one-loop corrections to the non-supersymmetric D3-brane
amplitudes, which agree with the known results in the literature.
