The 29-year-old was last seen by his friend at 12.15am on Friday when he left the York Central Travelodge on Piccadilly where they were staying the night.
Mr Johnson did not return to the hotel and he failed to turn up for work in Skipton on Friday evening. His mobile phone is also going to answer phone and he has not been in contact with his family, which is out of character.
Extensive police enquiries are ongoing to trace Rory and to establish his movements on Thursday evening and into the early hours of Friday morning.
His friend said they were in The Postern Gate Wetherspoon pub from around 11.30pm on Thursday, but explained that Mr Johnson headed back out after returning to the nearby Travelodge for a short time at around midnight.
One line of enquiry is that Rory may have got into difficulty while walking near the River Ouse in the City Mills and Skeldergate Bridge after midnight.
The Humberside Police Underwater Search Unit are carrying out searches in the Ouse throughout today to assist the missing person enquiry.
People who recall seeing Rory or someone matching his description in York on Thursday evening or Friday are urged to get in touch with the police without delay.
Mr Johnson is white, 29, 5ft 11in tall, slim build, with has short blond hair. He was wearing a round-neck black top, blue jeans and white and navy trainers.
Anyone who can help is urged to call North Yorkshire Police on 101, select option 1, and speak to the Force Control Room. Please quote reference number 12150207141.
Mr Johnson’s family are being supported by the police while enquiries are ongoing.