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Nope, it's not a deleted scene, it's actually part of the alternate ending seen in some countries.
In some (guess in the one you've seen), after the battle of the Mounds Conan goes back to the Mountain of Power all alone to kill Thulsa.
In the large ending, he goes back acompanied by the Princess, who goes first and passes in front of the guards that Conen then kills one by one with the broken sword.
After he cutts Thulsa's head off, the orphans throwh their candles to the fountain and we see Conan sat in the stairs, in the "thinker" pose, meditating about all that has happened. The Princess looks at him.
Then Conan holds the lamp and throws it, burning the place. Before he leaves, the Princess looks at him like he is a new God, and postrates to him. Conan doesn't look interested in the girl, and goes away, but then stops and, very serious, gives his hand to her and she takes it.
Then they disspear in the distance, Conan is carrying her in his arms.
All this is way better explained here, though:
http://www.conancompletist.com/EN/finale01.htm