Traditionally related to the same root as pars, possibly from Proto-Indo-European *perh₂- (“to sell”), which also gave the Ancient Greek πόρνη (pórnē, “prostitute”), and πέρνημι (pérnēmi, “to sell”).
De Vaan offers an alternative etymology where portiō would instead be a dissimilated and syncopated compound of prō + ratiō: prō ratiōne > prōrtiōne > portiōne, an adverbial phrase from which the noun portiō would be back-formed. If this etymology is correct, portiō would be unrelated to pars.