check out this link for some theories this kind of thing:
http://www.red3d.com/cwr/steer/It has some java examples that you can view in your browser, and some explanations on how they work. You'll probably want the 'wander' algorithm.
Basically it puts an imaginary full circle in front of your 'ant', and pick a random spot on the circumference of this circle.
You steer your ant in a straight line towards this spot.
However, each step the ant takes, the circle moves one step away as well in the same direction (so it always stays ahead of you), and your selected spot will randomly move either left or right a step, following the circumference of the circle.
This acts as a directional vector: you keep aiming your ant in a direct line towards this spopt on the edge of the circle.
Because of the shape of the arch projected in front of you, you essentially 'dampen' then randomness, movements gets smoothed out over time. The wandering will appear much more natural and less epileptic than a pure 'turn left, turn right, turn right, etc.)
The size of the circle will affect how jittery the movement will be: a small circle will lead to more erratic wandering, while a huge circle will not deviate much from its cource. Pick a size that suit your needs.
(A full circle will cause your ant to wander all over, you can make it more restrictive by using a partial arch instead of the entire circle.)
Anyway, it's a bit hard to describe -- follow the link for a visual example.