McDonald says security camera footage will show a consensual sexual encounter occurred in his hot tub.
Police say the woman doesn't recall any sexual encounters and reported blacking out after drinking alcohol and falling at McDonald's home.
She said she went to police after waking up naked next to McDonald.
The 49ers cut McDonald in December after learning of the allegation. The Santa Clara County district attorney is considering whether to file criminal charges.
McDonald's lawyer says the unresolved accusations are preventing the defensive lineman from signing with an NFL team.
"Because there has been no formal action, in the eyes of NFL teams, the unresolved threat of charges being filed against him, even though factually unfounded, continues to present a roadblock to this remarkable athlete being able to move forward in his career," defense attorney Steve DeFilippis said.
The 49ers released McDonald on Dec. 22, citing a pattern of behavior and off-field issues.
In November, the Santa Clara County district attorney's office announced it had declined to file charges against the defensive lineman in a separate domestic violence investigation.
The lawsuit filed Monday in Santa Clara County seeks unspecified damages.