Although unusual in this context, there is the verb libate:
: to pour out a libation or make libation to
1 : to make libation
2 : to drink alcoholic drink
// sat up with three libating guests who would not leave
In theory, as a transitive verb, you should be allowed to say:
If I am hungry, I say feed me. If I am thirsty, I say libate me.
At least in terms of its association with libation, the word would be understood.
In fact, the first Google hit I got on libate me returned Libate Me with Google Maps:
The New Belgium Brewing Company's Libation Location Map uses Google Maps to help you find the nearest locations that stock their many beers.
Using the map you can enter a location and select from the many beers on offer from New Belgium Brewing. You can even select the distance that you are prepared to travel to get your favourite tipple. The Libation Location Map then shows you all the stores near by where you can purchase your beer.
Perhaps ironically, the link to the Libation Location Map it mentions returns a 404 error.
Shortly after that on Google are hits on the LGBT+ poem A Queerification, by Regie Cabico, which includes the lines:
libate me in halos
heal me in halls of femmy troubadors
Needless to say, however, while libate does appear to be a valid verb that can be used in this way, it's extremely uncommon and, due to this, would not be at all idiomatic.
Note, too, that it doesn't seem to exist at Oxford Dictionaries, so it may only be a US verb. But Oxford Dictionaries does say this under its definition of libation:
Late Middle English: from Latin libatio(n-), from libare ‘pour as an offering’.
(The OED itself might provide an entry for libate, but I don't have access to it.)