A relatively literal translation would be votum facere (literally, “make a prayer”), although it generally seems to be used in the plural, e.g. Cic. Pro Milone 76:
Imperium ille si nactus esset, omitto socios, exteras nationes, reges, tetrarchas; vota enim faceretis ut in eos se potius immitteret quam in vestras possessiones, vestra tecta, vestras pecunias.
If he had obtained power, I'm not talking about our allies, foreign nations, kings and princes; for you would have made prayers that he would hurl himself at them rather than at your property, your houses and your money.
Or In Catilinam 2, 18:
Sed hosce homines minime puto pertimescendos, quod aut deduci de sententia possunt aut, si permanebunt, magis mihi videntur vota facturi contra rem publicam quam arma laturi.
But I do not think we have to be afraid of those people at all, because they can either be talked out of their ideas, or, if not, it seems more likely to me they'll make wishes than pick up arms against the state.
Literally, a votum is a pledge made to a deity – with the implication that this is done to persuade the god to grant a wish, and from there, the word took on the wider meaning of heartfelt wishes, which one hopes will be granted by divine intervention. Another rather banal example from a letter of Cicero's to one M. Mario:
Nos hic in multitudine et celebritate iudiciorum et novis legibus ita distinemur ut cottidie vota faciamus ne intercaletur, ut quam primum te videre possimus.
I am being held up here with so many and so well-attended trials and with new laws that I am praying daily they won't be inserting days in the calendar [this was occasionally done by the religious authorities!] so that I can visit you as soon as possible.
Presumably Cicero did not really kneel down before his lares daily in the service of this matter, but maybe he did cross his fingers when he glanced at the calendar…