Rapp, who was 14 at the time, alleges that Spacey, aged 26 at the time, made a sexual pass at him while they were both appearing in shows on Broadway in 1986.
Following the accusations, Spacey responded on Twitter saying he did not remember the alleged incident but attributed it to "deeply inappropriate drunken behaviour".
Spacey also addressed his sexuality by coming out as gay, which many have branded as an attempt to deflect from the serious sexual harassment allegations made against him.
Netflix has now responded with the decision to end House Of Cards after its sixth season.
In a joint statement obtained by Deadline, Netflix and production company Media Rights Capital confirmed the end of the show, saying they "are deeply troubled by last night’s news concerning Kevin Spacey."
"In response to last night’s revelations, executives from both of our companies arrived in Baltimore this afternoon to meet with our cast and crew to ensure that they continue to feel safe and supported," the statement continued. "As previously scheduled, Kevin Spacey is not working on set at this time."