  We show that automatic sequences are asymptotically orthogonal to periodic
exponentials of type $e_q(f(n))$, where $f$ is a rational fraction, in the
P\'olya-Vinogradov range. This applies to Kloosterman sums, and may be used to
study solubility of congruence equations over automatic sequences. We obtain
this as consequence of a general result, stating that sums over automatic
sequences can be bounded effectively in terms of two-point correlation sums
over intervals.
