Here is the etymology of the word:

libation

1382, “pouring out of wine in honor of a god,” from Latin. libationem (nom. libatio) “a drink offering,” from libare “pour out (an offering),” from PIE *(s)leib- “to pour, drop” (cf. Gk. leibein “to pour, make a libation”), an enlargement of base *lei- “to pour, to flow” (cf. Skt. riyati “to let run;” Gk. aleison “a wine vessel;” Lith. lieju “to pour,” lytus “rain;” Hitt. lilai- “to let go;” Alb. lyse, lise “a stream;” Welsh lliant “a stream, a sea,” llifo “to flow;” O.Ir. lie “a flood;” Bret. livad “inundation;” Gael. lighe “a flood, overflow;” Goth. leithu “fruit wine;” O.C.S. liti, lêju, Bulg. leja “I pour;” Czech liti, leji, O.Pol. lic’ “to pour”). Transf. sense of “liquid poured out to be drunk” is from 1751.

It could be used subtlely in writing to mean an offering, but most people would not catch the inference.

Some older people might ask; “will you have a libation?” meaning will you have a drink?

This is also done as a form of prayer or for blessings and its usually done with the very first drop from the bottle or glass.