No, an alt attribute (it would be an attribute, not a tag) is not allowed for an a element in any HTML specification or draft. And it does not seem to be recognized by any browser either as having any significance.
It’s a bit mystery why people try to use it, then, but the probable explanation is that they are doing so in analog with alt attribute for img elements, expecting to see a “tooltip” on mouseover. There are two things wrong with this. First, each element has attributes of its own, defined in the specs for each element. Second, the “tooltip” rendering of alt attributes in some ancient browsers is/was a quirk or even a bug, rather than something to be expected; the alt attribute is supposed to be presented to the user if and only if the image itself is not presented, for whatever reason.
To create a “tooltip”, use the title attribute instead or, much better, Google for "CSS tooltips" and use CSS-based tooltips of your preference (they can be characterized as hidden “layers” that become visible on mouseover).