Because its Slavic etymology, it is clear the word was borrowed from Russian-Ukrainian (both languages have this word) or from some South-Slavic language (Bulgarian has it also). The root is "čaša" - "bowl, cup" + diminutive suffix "-ka". The Slavic word is related to Old Slavic "česati" "to scratch, to carve" (because utensils were made by cutting and carving wood). It is not connected to similar sounding word "ceai" tea.
These official Romanian dictionaries say is was exactly Russian:
Dicționarul explicativ al limbii române, ediția a II-a 1998
Dicționar universal al limbei române, ediția a VI-a 1929
Dicționarul limbii române moderne 1958
Noul dicționar explicativ al limbii române 2002
But "Dicționarul etimologic român 1958-66" shows general Slavic as a source and compares it with Bulgarian and Polish but not Russian or Ukrainian.
Probably, Ukrainian language wasn't even standardized when this word was borrowed.
Can you show a dictionary where exactly Ukrainian not Russian, was shown as a source?