The use of to after acquiesce was formerly regarded as incorrect, but is now acceptable
Word Origin
C17: from Latin acquiēscere to remain at rest, agree without protest, from ad- at + quiēscere to rest, from quiēsquiet
Word Origin and History for acquiesce
v.
1610s, from Middle French acquiescer (16c.), from Latin acquiescere "to become quiet, remain at rest," thus "be satisfied with," from ad- "to" (see ad-) + quiescere "to become quiet," from quies (genitive quietis) "rest, quiet" (see quiet (n.)). Related: Acquiesced; acquiescing.