  Non-local theories of gravity are considered extended theories of gravity,
meaning that when the non-local terms are canceled out, the limit of General
Relativity (GR) is obtained. Several reasons have led us to consider this
theory with increasing interest, but primarily non-locality emerges in a
natural way as a side effect of the introduction of quantum corrections to GR,
the purpose of which was to cure the singularity problem, both at astrophysical
and cosmological level. In this paper we studied a peculiar case of the so
called Deser-Woodard theory consisting in the addition of a non-local term to
the Hilbert-Einstein lagrangian, and we derived for the first time contraints
on the dimensionaless non-local parameter A by exploiting the predicted
gravitational wave emission in three binary pulsars, namely PSR J1012+5307, PSR
J0348+0432 and PSR $J1738+0333. We discovered that the instantaneous flux
strongly depends on A and that the best constraints (0.12 < A < 0.16) come from
PSR J1012+5307, for which the GR prediction is outside the observational
ranges. However, since for PSR J1012 + 5307 scintillation is suspected, as
emerged in a recent census by LOFAR, corruptions in pulsar timing could be
hidden. We finally comment on the usability and reliability of this type of
test for extended theories of gravity.
