Otsuka came to the United States after several years of pitching in the Japanese League when his former team, the Chunichi Dragons, used the posting system to solicit bids from MLB clubs for the right to negotiate with him.

Otsuka made his major league debut April 6, 2004 against the Los Angeles Dodgers, earning the loss after giving up a walk-off single to Robin Ventura.

Otsuka took over the role as the closer for the Rangers during the 2006 season, replacing Francisco Cordero, and recorded 32 saves while posting a 2.11 ERA.

With the trade of Gagne to the Boston Red Sox, Otsuka assumed the closer's role again.

On 26 September, Otsuka was unveiled as the pitching coach for the U-23 Japanese national team for the 2016 WBSC U-23 World Cup.