Rules for divine ascension in D&D existed when this book was released, but not necessarily for ascension in this exact manner.
The version of the text I can find places this character's apparent divine ascension in Chapter 3 of The Hammer of the Gods, "Book" 1 of Test of the Twins, the third published book of the Dragonlance Legends trilogy:
"What does it mean?" asked Tas, rubbing his eyes and staring sleepily up at the stars,
only half awake.
"It means Raistlin succeeded," Caramon answered with an odd mixture of fear, sorrow, and pride in his voice. "It means he entered the Abyss and challenged the Queen of Darkness and—defeated her!"
"Not defeated her, Caramon," said Tas, studying the sky intently and pointing. "There’s her constellation, but it’s in the wrong place. It’s over there when it should be over here.
"Raistlin won," Caramon said with a soft sigh. "He’s what he wanted to be—a god. And now he rules over a dead world."
That novel trilogy came out in 1986, which is the year before the first Dragonlance-specific sourcebooks were released (Dragonlance Adventures and Leaves from the Inn of the Last Home, neither of which mention rules for divine ascension).
The only edition of D&D at that time which specifically described ascension to divinity was Advanced Dungeons & Dragons 1st edition. In particular, Deities and Demigods (1980) included rules for divine ascension:
As study of the various mythologies will show, it is remotely possible for mortals to ascend into the ranks of the divine. However, there are certain requirements that must be fulfilled before such a thing could happen.
Those requirements are to be of exceptionally high character level, to have raised one's ability scores to be exceptionally high, to have a body of worshippers, and to be a faithful follower of one's patron deity.
However, the Dragonlance character in question does not appear to use this method or meet these requirements, suggesting that it was an original invention for that novel, although it may indeed have been inspired by Deities and Demigods.
BECMI Set 5: Immortals Rules was released in 1986, which includes rules on ascending to become an Immortal, although that is not specifically the same thing as a deity. The requirements for such ascension are vaguely defined: in one description, the player character must complete a challenge from an existing Immortal.
Later editions of Dungeons & Dragons, released after the novel series in question, did indeed include rules for ascending to divinity in various ways, including by defeating another deity.
D&D third edition's version of Deities and Demigods (2002), on p.219, opens up divine ascension to many possible methods. The DM chooses whether or not ascension is possible, and if so whether it is acquired through heroic death, earned by certain deeds, stolen from other deities, taken from slain deities, imparted willingly by existing deities, or taken from some source.
The D&D third edition Dragonlance sourcebook Legends of the Twins references Raistlin's ascension, although it does not provide rules for player characters to achieve the same.
Third Day, Fifthmonth, 356
Raistling emerges from the portal in the Tower of High Sourcery in Palanthas, followed by Tahksis. While the Battle of Palanthas rages outside, Raistlin slays the Dark Queen. Absorbing her power, he departs Krynn to do battle with the gods.
Twenty-Eighth Day, Seventhmonth, 356
Raistlinites appear for the first time, in Beacon on the north shores of Northern Ergoth.
Raistlin absorbing power from another deity and ascending before having any followers is inconsistent with the AD&D 1st edition Deities and Demigods rules which existed at the time the Dragonlance Legends were written.
Legends of the Twins also references the Kingpriest Beldinas Pilofiro's attempt to ascend to divinity:
By 40 PC, the last Kingpriest, Beldinas Pilofiro, had decided that as ruler of all Ansalon — and since he sat in judgement of over all men — he must therefore be a god. He began plotting his full ascension to godhood.
In an alternate history of Krynn, that book describes that character's ascension:
In binding the power of Paladine to his own spirit, the Kingpriest ascended to be come the Godpriest.
The Kingpriest summons Paladine and demands that the god grant him the power to complete the cleansing of the world. When Paladine refuses, the Kingpriest binds the god's spirit to his own, ascending to near-godhood and sparking the eternal Godspyre at the heart of the temple.