  The charge asymmetry has been measured using $19,039~W$ decays recorded by
the CDF detector during the 1992-93 run of the Tevatron Collider. The asymmetry
is sensitive to the ratio of $d$ and $u$ quark distributions to $x<0.01$ at
$Q^2 \approx M_W^2$, where nonperturbative effects are minimal. It is found
that of the two current sets of parton distributions, those of Martin, Roberts
and Stirling (MRS) are favored over the sets most recently produced by the CTEQ
collaboration. The $W$ asymmetry data provide a stronger constraints on $d/u$
ratio than the recent measurements of $F_2^{\mu n}/F_2^{\mu p}$ which are
limited by uncertainties originating from deutron corrections.
