I agree with the comments that there is no indication of a problem in this plot.
That being said, even if you had more data, deviance residuals wouldn't be a good way to test for such a dependence, because also a perfectly fitting binomial model may exhibit inhomogeneous deviance residuals.
What works is the simulation approach suggested by Glen_b. This is implemented in the DHARMa R package, which uses simulations from the fitted model to transform the residuals of any GL(M)M into a standardized space. Once this is done, you can visually assess / test residual problems such as deviations from the distribution, residual dependency on a predictor, heteroskedasticity or autocorrelation in the normal way. See the package vignette for worked-through examples.