The West Brom and Republic of Ireland forward, who made 17 appearances for the Blades in the 2019-20 season, first tested positive in November last year and then again in August, meaning he had to sit out last month's World Cup qualifiers.
The 26-year-old is on international duty with the Republic of Ireland, alongside Sheffield United trio John Egan, Enda Stevens and Conor Hourihane.
When asked if he had received the vaccine, Robinson responded: "I haven't been vaccinated, no. That's my choice at this moment in time.
"It's obviously annoying that I've caught it twice but I haven't been vaccinated. Further down the line I could change my mind and want to do it, but at this moment in time I haven't been vaccinated, no."
Robinson did not want to discuss his reasons for opting against the vaccine and doesn't feel anyone should be forced into taking it.
He added: "I just haven't, I just haven't done it. I think it's your personal choice and my choice at this moment in time, I haven't been vaccinated.
"I know, as you said, there are managers and people that will want you to do it, which is right in their way, the way they think, but everyone has their choice on what they want to do. I wouldn't force people to do it, it's your choice and your body."
Republic of Ireland manager Stephen Kenny says he has encouraged his staff and players to get the vaccine but admits it would be a step too far to only select players who have received both jabs.
He said: "I was very happy to be (vaccinated) myself and encouraged staff and players. Of course it seems like the most sensible thing to do, and the safest with regard to our environment.
"There are a lot of myths and a lot of issues around virility that people are concerned about and other issues, you know, and I do think it is complex. I am not a medical expert, but I do trust the experts and I do think it is better to be double-vaccinated."