John Allan, 43, from Ayr, got his victim to help him carry a beer keg and then took her into his home where he raped her.
He claimed that the woman had consensual sex with him and she instigated it, but the jury did not believe his explanation and found him guilty of rape.
The rape took place at Allan’s flat in Murray Street, Ayr, Ayrshire, on June 19, 2017.
The woman was unable to give evidence in court because of her condition and the jury was read a statement she gave to specially trained police officers, and shown a video taped interview made just days after the rape.
The woman told police: “I went for a walk about 5.15am and on the way back I bumped into a man.
“He was on his own and carrying something. I didn’t know the man, but he said he knew me and I said ‘I have dementia,’ and I told him I was 61. He said ‘you look 51.’”
The woman said that inside the flat Allan began talking about sex and she added: “I didn’t know what he was talking about. I told him I wanted to go home.
“He undressed me and then himself and put me into the bed. I didn’t understand what was happening”
The woman said that after Allan raped her, she dressed and left the flat. She said: “I didn’t know where I was. I was upset and crying.”
When she eventually arrived home the woman told relatives what had happened and the police were contacted.
When Allan was quizzed by police he said he had had consensual sex with the woman.
In evidence he was asked by prosecutor Ashley Edwards QC: “Did you at any point ask her if she wanted to have sex with you,” and replied: “No. It was just spontaneous sex.
Miss Edwards then said: “Did she tell you she was 61,” and Allan replied: “I wasn’t paying much attention to what she said.”
The prosecutor then asked: “What made you think she was coming into the house for sex,” and Allan said: “Well she wasn’t coming in for anything else. There was nothing else to come in for. There was no other reason was there. I just thought my luck was in. I thought I’ve got a click.”
Allan claimed he only knew his victim had dementia when the police told him.
Judge Lady Scott remanded Allan in custody and deferred sentence until next month for background reports.
She also placed Allan on the sex offenders’ register.