He could do so (literally) blindfold without much effort. But the question is about Fischer versus Carlsen.
Based simply on the accuracy of play, Fischer, despite being one of the greatest players in chess history, would have to up his game significantly from what he needed to win the world championship in 1972. (I like the 1992 match, but the standard of play was not much different to 71-72).
Players get better as time goes forward. That's just how things work. If FIscher was born the same year as Magnus then he would probably beat him given how obsessive Fischer was over chess. Fischer would probably be the closest thing to the best super computer out there if he put the same amount of effort into it. However, even Kasparov said that the Spassky vs Fischer rematch in 92 was "very much the chess of 1972." That indicates that chess theory has grown (which we all know it has), so Magnus would have close to 50 years of theory over Fischer. I'd like to say that Fischer would win, but I don't think he would under those circumstances.