Edit: We do not know. Seems like <PERSON> never bothered much with that clarification.
Still some estimation was done, you may take a look at this one (by maximedhiver): Atreides Military Forces on Arrakis - size?
The best hint is this:
"We don't have much time, as you well know. They'll be here with <PERSON> disguised as Harkonnens at the first opportunity. How many do you think they'll ship in, <PERSON>?"
"Four or five battalions all told, Sire. No more. Guild troop-transport costs being what they are."
"Then five battalions of Fremen plus our own forces ought to do it. 126
Let us have a few captive Sardaukar to parade in front of the Landsraad Council and matters will be much different—profits or no profits."
And <PERSON>'s later reflection:
For a full attack they'd expected no more than ten brigades.
We're told that an Imperial brigade is about 3,000 men. The strength of a battalion is never given, but in our world it apparently ranges between 300–1,000 men. So <PERSON>'s first estimate is somewhere in the 1,200–5,000 range, while his second is 30,000. Presumably his first "all told" number must only be counting the <PERSON>, while the second is the full Harkonnen force he expected. (Or it's an inconsistency.)
Given that the <PERSON> troops are supposed to be within a hair as good as the <PERSON>, that a Sardaukar is supposed to be a match for 10 regular conscripts, that they know the Fremen are formidable fighters (although they may not realize they're already almost a match for the Sardaukar), and that the Atreides apparently felt relatively confident of winning such a confrontation—but only with Fremen help—I would conclude that the Atreides troop strength on Arrakis matched:
The expected Sardaukar force (4–5 battalions) = 1,200–5,000
Plus one tenth of the expected Harkonnen force of 30,000 men = 3,000
Plus a bit, but not very much, more, say = 1,000–2,000
(To be reinforced by 4–5 Fremen battalions)
So probably somewhere in the range of 5,000 to 10,000 Atreides fighting men. That should be enough to give them a clear advantage in the attack they expected, while not enough that it wouldn't pose a genuine threat.
As you can see, this calculation depends heavily on an assumption that the Atreides troops are very superior to Harkonnen troops one-to-one. If this assumption does not hold, we might be talking 30,000 Atreides troops or more. 342