  We cross-correlate the positions of damped Lyman-$\alpha$ systems (DLAs) and
their parent quasar catalog with a convergence map derived from the Planck
cosmic microwave background (CMB) temperature data. We make consistent
measurements of the lensing signal of both samples in both Fourier and
configuration space. By interpreting the excess signal present in the DLA
catalog with respect to the parent quasar catalog as caused by the large scale
structure traced by DLAs, we are able to infer the bias of these objects:
$b_{\rm DLA}=2.6\pm0.9$. These results are consistent with previous
measurements made in cross-correlation with the Lyman-$\alpha$ forest, although
the current noise in the lensing data and the low number density of DLAs limits
the constraining power of this measurement. We discuss the robustness of the
analysis with respect to a number different systematic effects and forecast
prospects of carrying out this measurement with data from future experiments.
