Rogue/Magneto begins in “Uncanny X-Men” #269 (by Chris Claremont and Jim Lee). Rogue winds up in the Savage Land (a tropical region in Antarctica where dinosaurs still roam, as seen in season 2 of the original “X-Men” series). Magneto is also calling it his home and he saves Rogue from the personification of the Ms. Marvel half of her personality, which she absorbed from Carol Danvers (also semi-adapted in “A Rogue’s Tale,” minus Magneto).
They grow closer, especially since Rogue has temporarily lost her powers and can touch people. In “X-Men” #274-275, they team up to liberate the Savage Land from the evil Zala Dane. However, despite Rogue’s pleading with his better angels, Magneto executes Zala Dane, renouncing his previous turn to good and commitment to live by Xavier’s dream. Rogue leaves him before any relationship can begin.
This story happens at the tail end of Chris Claremont’s 17-year “X-Men” run (he was forced out by editor Bob Harras after issue #279). However, Rogue/Magneto wasn’t Claremont running out of ideas (he never really did). I can see why he thought to bring them together; they’re both reformed villains, after all. Plus, this actually happened just before Rogue and Gambit’s relationship began (Gambit was introduced only in “Uncanny X-Men” #266 and he only started flirting with Rogue in Jim Lee’s relaunched “X-Men,” which was the aesthetic influence on the cartoon).
While nothing ever actually happens between the two here, later writers did not forget Rogue and Magneto’s connection. In the alternate “Age of Apocalypse” timeline, Rogue and Magneto are married, with Erik using the same electromagnetic trick to let Rogue touch him as in “X-Men ’97.”