  Recently, the CDF collaboration reported a new measurement of the $W$ boson
mass $M_W = 80.4335 \pm 0.0094$ GeV, which shows a $\sim 7\sigma$ deviation
from the standard model prediction $80.3545 \pm 0.0057$ GeV obtained by the
electroweak (EW) global fit. This deviation can be explained by new physics
generating moderate EW oblique parameters $S$, $T$, and $U$. In this work, we
use the loop corrections induced by some extra EW multiplets to explain the CDF
$M_W$ anomaly. The lightest neutral particle in the multiplets can also serve
as a candidate of cold dark matter (DM). We consider two such models, namely
singlet-triplet scalar DM and singlet-doublet fermionic DM models, and perform
numerical scans to find the parameter points accounting for the $M_W$ anomaly.
The constraints from the correct DM thermal relic density and direct detection
are also taken into account. We find the parameter points simultaneously
interpreting the $M_W$ anomaly and satisfying the DM requirements in the former
model, but do not find such parameter points in the latter model.
