Prosecutor Rachael Landin said: "In response to some questions in relation to whether matters would hurt he said his penis wasn't very big."
Smith, of North Shields, Tyne and Wear, was arrested when he turned up at Central Station in Newcastle to meet the girl but was confronted by Dark Justice, who filmed the meeting.
He pleaded guilty to attempting to meet a child after grooming and breach of registration requirements by failing to tell the authorities where he was living.
He was jailed for a year and eight months and ordered to serve an extended licence period after he is freed. He must now also sign the Sex Offenders Register for life.
Judge Jeremy Freedman told him: "You clearly intended there should be full sexual intercourse, even though you believed the girl to be a 13-year-old child who had no sexual experience of any sort.
"The person you in fact communicated with was with an organisation called Dark Justice, who track down people such as you, who attempt to groom children though social networks.
"It is deeply concerning you have not changed your behaviour in any way, despite being on a sex offenders treatment programme.
"You have no real insight into the harm your actions could potentially cause.
"I think you are intent, if left to your own devices, on having sexual relationships with young people, even though you know very well it was wrong to so do and very harmful to potential victims of such offences."
Smith claimed he was "lonely" when he started the online conversation and had been "flattered".
