LATIN DICTIONARYLexicon Latīnum
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“arbitrate” in Latin

The English word arbitrate itself goes back to Latin arbiter, through arbitratus.

Riddle & Arnold A Copious and Critical English–Latin Lexicon, 1864

arbitrate
decide judicially, disceptare aliquid: deceruere aliquid, or de re, or absolutely dijudicare aliquid (these three are also used of arbitration by the sword, ferro): judicare aliquid or de re: decidere aliquid or de re: statuere, constituere aliquid. To arbitrate in any matter, affirmare de re: in a dispute, controversiam disceptare, decernere, dijudicare: de controversia decidere, statuere, constituere.
Act as arbiter, arbitri partes suscipere: esse arbitrum or disceptatorem (inter aliquos). Vid: “to be an arbiter,” under ARBITER.

Quick answer

What is the Latin word for arbitrate?
The usual Latin words for “arbitrate” are statuō, disceptātor, ferrum. The right choice depends on the sense; see the distinctions below.

Entry from J. E. Riddle & T. K. Arnold, A Copious and Critical English–Latin Lexicon (rev. C. Anthon, New York: Harper, 1864), digitised by Fergus J. P. Walsh, CC BY-SA 4.0; Latin markup adapted by latindictionary.co.