The woman, a 24-year-old named only as Effie, made the allegations during a virtual press conference held by high-profile US lawyer Gloria Allred.
In a statement to the PA news agency, Hammer's lawyer Andrew Brettler described the allegations as "outrageous" and said his client "welcomes the opportunity to set the record straight".
The accuser broke down while reading a prepared statement, alleging she first met Hammer, 34, on Facebook in 2016.
She alleged he raped her for four hours in 2017 and slammed her head against a wall.
She said she first had contact with Hammer on Facebook when she was 20, adding: "I fell in love with him instantly."
Effie said Hammer was "employing manipulation tactics in order to exert control over me, until I started to lose myself".
She said he would "test my devotion to him, finally removing and crossing my boundaries as he became increasingly more violent".
Effie accused the actor of abusing her "mentally, emotionally and sexually".
She said: "On April 24 2017, Armie Hammer raped me for over four hours in Los Angeles, during which he repeatedly slapped my head against a wall, bruising my face."
Effie said their last interaction was last year.
Mr Brettler has denied the allegations on behalf of his client.
He included a text, allegedly from the accuser, claiming it "undermines and refutes" the rape allegation.
Mr Brettler's statement read: "As recently as July 18, 2020, (the accuser) sent graphic texts to Mr Hammer telling him what she wanted him to do to her. Mr Hammer responded making it clear that he did not want to maintain that type of relationship with her. The screenshot below is just one of hundreds (the accuser) sent to Mr Hammer.
"It was never Mr Hammer's intention to embarrass or expose (the accuser's) fetishes or kinky sexual desires, but she has now escalated this matter to another level by hiring a civil lawyer to host a public press conference.
"With the truth on his side, Mr Hammer welcomes the opportunity to set the record straight.
"From day one, Mr Hammer has maintained that all of his interactions with (the accuser) - and every other sexual partner of his for that matter - have been completely consensual, discussed and agreed upon in advance, and mutually participatory.
"(The accuser's) attention-seeking and ill-advised legal bid will only make it more difficult for real victims of sexual violence to get the justice they deserve."
When asked if Effie would be pressing charges, Ms Allred said: "Effie is providing what she thinks might be relevant to law enforcement and then it is for law enforcement and the prosecutor to decide if there is sufficient evidence to pursue it.
"I will only say that Effie has the courage to co-operate in any investigation that may be taking place."
The Los Angeles Police Department told PA it has opened a sexual assault investigation following a rape claim against Hammer.
A spokesman said officers were contacted by an attorney "representing a female in the community" on February 3.