Rodriguez will look to extend his 10-fight win streak at the UK-based event, being headlined by Strikeforce contender Paul Daley vs. DEEP champion Yuya Shirai for the vacant BAMMA welterweight strap.
Rodriguez (45-11), who last year expressed interest in returning to the UFC as a light heavyweight, has remained unbeaten since a Reality Combat bout in July 2009. The 33-year-old's most recent fight was a unanimous decision over Daniel Tabera at Israel FC last November.
McSweeney (4-6), a British striker with all four wins via (T)KO, was released by the UFC this past fall following losses to Travis Browne and Fabio Maldonado in 2010. His lone Octagon win was against Darrill Schoonover at the TUF 10 Finale in December 2009.
Three more main card bouts will be added to BAMMA 5.