Leeds paid an undisclosed fee to sign the 26-year-old from Red Bull Salzburg on a five-year-deal last summer.
The Denmark full-back went on to score three goals in 30 games as the club were relegated from the Premier League.
Kristensen, who has made 15 international appearances for Denmark, has followed Spanish centre-back Diego Llorente in making a loan move to the Stadio Olimpico.
Llorente initially joined Roma on loan in January but has returned to the Italian side for the 2023-24 season.