Is there a way to reveal invisible characters in Awesomenauts?
Update: The 1.03 patch for the PC version has added a new character, Gnaw, who has an attack called Acid Spit which makes it possible to track enemies while they are cloaked (though it doesn't remove the cloak effect itself). If you watch this Youtube video of Bunnymancer playing Gnaw, you'll see him hitting an enemy Leon with Acid Spit and tracking him even though he is cloaked.
Original Answer: No, there is no way to reveal invisible enemy players.
Currently, Leon's Cloaking Skin is the only ability that allows players to become hidden from the opposite team, and the only way to end the effect is for the invisible player to take an action other than moving or jumping.
The invisible Leon will still take damage if hit by attacks, but this will not remove the invisibility.
There is a passive way of doing this - by affecting Leon with poisoning, slowing or some other effect that shows some thumbnail above character.
There is also a neat trick usable at AL Station 404. Between the front turret and the top turret behind there is an area with yellow floor that lights up when you step on it. It actually saved me once or twice because I could see invisible Leon approaching me by looking at the floor lighting.
Upd1: another trick, barely usable though. Invisible characters still collect solar 8p. So, if there is solar lying around, you might notice invisible's presence.