וַתָּ֣שַׁר דְּבוֹרָ֔ה וּבָרָ֖ק בֶּן־אֲבִינֹ֑עַם בַּיּ֥וֹם הַה֖וּא לֵאמֹֽר׃
Then sang Deborah and Barak the son of Abinoam on that day, saying:
Metzudat David on Judges
Saying: That is to say that the Children of Israel will say it.
Radak on Judges
And Devorah and Barak son of Avinoam sang: Because Devorah is the central actor [she is mentioned first]. It is like (Numbers 12:1), "Miriam and Aharon spoke about Moshe."