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Mike (a PC) takes the mild consequence Jittery from a ghost's mental attack, granting the ghost a tag on that aspect. Soon after, Andy (another PC) rolls Intimidate (as a social attack) to tease Mike about being so jumpy.
The rules make no provision for this, but you could do that without breaking the game when you judge it an appropriate thing to do.
If you're unsure, err on the side of not doing it – a consequence of allowing a PC to use the free tag as if they were the ghost's ally is that the ghost is deprived of the free tag. Doing this too casually could be exploited by the players to strategically "use up" in harmless ways the free tags that their enemies should be enjoying. If in doubt, make the PC pay for it with Fate points as normal.
Assume that the rights to that tag rest with the player of the ghost in question ie. the GM in this case. It is the GM's right to use and offer it as he sees fit, even for actions by other characters. It is not tied to the ghost in any manner.
Mechanically, if Andy wants to compel an action from Mike, he should give Mike one of his Fate points. That also seems like the best way to handle it thematically. Also, using Intimidate to "give Mike a hard time" isn't really enough reason to compel a Fate Point in the first place, unless Andy is granting himself an extra +2 on his Intimidate die roll or if Mike concedes the roll because of Andy's invocation of the aspect.
The bottom line is: any time you use a player's aspects against him, they get Fate points for it. The only exception is if you have a free tag to use. Andy doesn't have that free tag, the ghost does. Unless you can justify in some what the ghost giving Andy the tag (and I'm not seeing it here), he has to spend the Fate point, and, as noted, give it to Mike.
