  We show that the distributions occurring in the geometric and spectral side
of the twisted Arthur-Selberg trace formula extend to non-compactly supported
test functions. The geometric assertion is modulo a hypothesis on root systems
proven when the group is split. The result extends the work of Finis-Lapid (and
M\"uller, spectral side) to the twisted setting. We use the absolute
convergence to give a geometric interpretation of sums of residues of certain
Rankin-Selberg L-functions.
