Yes. In the prequel novella "The Hedge Knight", the first of the three prequels included in the collection "A Knight of the Seven Kingdoms," it is established that any knight can make a knight.
"Hmpf." The man Plummer rubbed his nose. "Any knight can make a knight, it is true, though it is more customary to stand a vigil and be anointed by a septon before taking your vows."
"The lad has the truth of it," said Ser Lyonel Baratheon. "Do it, Ser Duncan. Any knight can make a knight."
Indeed, this happens later in the story, when Ser Lyonel knights Raymund Fossoway.
This is also brought up briefly in A Storm of Swords when Arya meets Beric Dondarrion and his "Brotherhood without Banners":
"Knights?" Clegane made the word a sneer. "Dondarrion's a knight, but the rest of you are the sorriest lot of outlaws and broken men I've ever seen. I shit better men than you."
"Any knight can make a knight," said the scarecrow that was Beric Dondarrion, "and every man you see before you has felt a sword upon his shoulder. We are the forgotten fellowship."