We'll introduce every song that's ranked in on The Best Ten!

Literal

The Best Ten [into-に] ranked-in songs [obj-を] all introduce!

Classic TV show announcement. ザ・ベストテン is 'The Best Ten,' a legendary Japanese music ranking TV program (1978–1989) that counted down the top ten songs each week. ランクインする ('to rank in, to make the chart') is a Japanese-English verb. ランクインした is a past-tense relative clause modifying 曲. 全て ('all, everything') is the all-inclusive modifier. Nostalgic for older Japanese viewers.