If he chose to do so, he most certainly could. Pope Pius IX adopted Edgardo Mortara.
Canon law does not directly address the issue. It would certainly seem contradictory to the essence of the celibacy commitment: freedom from familial obligations to fully serve the Church. However, there have been isolated cases in various parts of the world where bishops have granted permission for priests to adopt in particular situations. In the case of the Pope he needs no permission since he is the supreme judge (canon 1442).
