It seems so.
The most compelling evidence I've found (thanks to the Stoicism community on Reddit) is the following passage, quoting one of the Fox's lessons:
"Orual," she said, "you make me think I have learned the Fox's lessons better than you. Have you forgotten what we are to say to ourselves every morning? 'Today I shall meet cruel men, cowards and liars, the envious and the drunken. They will be like that because they do not know what is good from what is bad. This is an evil which has fallen upon them not upon me. They are to be pitied, not - '." She was speaking with a loving mimicry of the Fox's voice; she could do this as well as Batta did it badly.
Compare this with the following quote from Marcus Aurelius's Meditations, apparently "a significant source of the modern understanding of ancient Stoic philosophy":
Begin the morning by saying to thyself, I shall meet with the busy-body, the ungrateful, arrogant, deceitful, envious, unsocial. All these things happen to them by reason of their ignorance of what is good and evil. But I who have seen the nature of the good that it is beautiful, and of the bad that it is ugly, and the nature of him who does wrong, that it is akin to me, not only of the same blood or seed, but that it participates in the same intelligence and the same portion of the divinity, I can neither be injured by any of them, for no one can fix on me what is ugly, nor can I be angry with my kinsman, nor hate him.
The Fox has also been counted as representing Stoicism by a multitude of sources, from academics and journals, to blogs and critics, to popular sites and help pages. I'll quote this one in more detail:
The Fox, who becomes the tutor of Orual and Psyche, is a Stoic philosopher who has been captured in war and sold into slavery and by that means come to Glome. He is very definitely Stoic, because almost everything he says is standard Stoicism -- this book would be a fairly easy way to introduce the topic of Stoic philosophy. And at one point, Psyche, in the course of describing the Fox's teaching, gives what is in fact a close paraphrase of the opening of Book II of the Meditations of Marcus Aurelius. Marcus Aurelius is a nearly exact contemporary of Apuleius, since he also died in AD 180 and we know that the Meditations were more or less composed in the last decade of his life. It is not, of course, plausible that Lewis is suggesting Marcus Aurelius as the source of the Fox's teaching, but it is entirely plausible to suggest a common influence. The Emperor was only writing a sort of philosophical notebook for himself, and often quotes and borrows from other authors in various ways. If one assumed that Marcus Aurelius was quoting or alluding to someone, then, one would take the Fox and the Emperor as having a common link somewhere.