Philip Shorten is also accused of inciting the teenager to commit sexual acts using an internet webcam, and organising for others to view along with him.
He travelled to Northern Ireland four times to meet the girl in hotels when she was aged between 15 and 16, it was claimed.
Shorten, 49, of Flagstaff Green, Gosport, faces a total of 11 counts of sexual offences against a child.
The charges, allegedly committed between July 2010 and February 2011, include rape, making and possessing an indecent photograph of a child, and arranging the involvement of a child in pornography.
He is further accused of setting up an online account to involve a child in sexual activity, intentional sexual touching of a girl aged under 16, and incitement to engage in sexual activity.
Other counts against him involve meeting a child following sexual grooming and intentionally causing her to look at a sexual image.
Belfast Magistrates' Court heard Shorten met the girl last year through an online messaging service.
A detective constable said the pair at first engaged in normal online chats.
But he claimed the accused then incited her to carry out sexual acts on herself and to strip in front of a webcam while he viewed.
It was alleged that Shorten, calling himself Steve, further progressed to setting up an online account and providing details to the girl.
"He incited and arranged for the child to log on to that account using the password he gave," the officer said.
"The defendant had added others into that so they could also view the activities by the child at his request."
As the alleged offences continued Shorten travelled to Belfast four times to meet the girl in two different hotels, the court heard.
Police claimed he carried out various sexual acts and took photographs, knowing she was aged 15-16 at the time.
Communication between the pair ended following the alleged rape of the girl in February, according to the officer.
She claimed that after being informed detectives had her chat logs Shorten asked her to say she told him she was 18, and that he believed any references to a 15-year-old schoolgirl were purely role-play.
Opposing bail, the officer said the accused was well aware of her real age and posed a risk of re-offending.
"From the evidence available we believe the defendant systematically groomed this child online," he said.
He claimed Shorten had started out with "normal chit-chat" before "pushing the boundaries" on more sexualised conversations.
"There were pornographic links for the child to watch and describe to him as she was watching," he said.
"In the video interview she gave to police she talked about actually seeing and describes another male who she describes as an old man with a white beard."
An online paedophile investigation team from Hampshire Police are examining computers seized last week.
But Shorten has claimed other equipment was either lost, stolen or thrown out.
A defence solicitor said the accused denied the offences and had told police he believed the girl was over 18.
He added that Shorten had travelled to Northern Ireland and the Irish Republic for business interests, with any hotel visits at the end of these trips.
Bail was refused, despite a defence submission that Shorten could be released but banned from any internet access.
Deputy District Judge Philip Mateer ruled there was a risk of further offences.
He said that, according to the prosecution, Shorten had shown "deep-seated tendencies" because of the length of time over which the alleged offences were committed.
The accused was remanded in custody to appear again by video-link next month.
Mr Mateer added that the girl involved may have "some issues about her outlook on sexual activity" due to names she used on online accounts.