  Effect of structural disorder is investigated for an $XY$ pyrochlore
antiferromagnet with continuous degeneracy of classical ground states. Two
types of disorder, vacancies and weakly fluctuating exchange bonds, lift
degeneracy selecting the same subset of classical ground states. Analytic and
numerical results demonstrate that such an "order by structural disorder"
mechanism competes with the effect of thermal and quantum fluctuations. Our
theory predicts that a small amount of nonmagnetic impurities in
$\rm{Er_2Ti_2O_7}$ will stabilize the coplanar $\psi_3$ ($m_{x^2-y^2}$)
magnetic structure as opposed to the $\psi_2$ ($m_{3z^2-r^2}$) state found in
pure material.
