  We consider the critical behaviour of the continuous-time weakly
self-avoiding walk with contact self-attraction on $\mathbb{Z}^4$, for
sufficiently small attraction. We prove that the susceptibility and correlation
length of order $p$ (for any $p>0$) have logarithmic corrections to mean field
scaling, and that the critical two-point function is asymptotic to a multiple
of $|x|^{-2}$. This shows that small contact self-attraction results in the
same critical behaviour as no contact self-attraction; a collapse transition is
predicted for larger self-attraction. The proof uses a supersymmetric
representation of the two-point function, and is based on a rigorous
renormalisation group method that has been used to prove the same results for
the weakly self-avoiding walk, without self-attraction.
