If its royal icing that you made it is very thin as a general rule. Boulangere and ATG117 are correct you can thicken by adding more powdered sugar and the cream cheese is a wonderful idea. I sometimes pipe a border around the cookie to hold the royal icing in place when it floods the cookie. You can buy it in tubes pre-made or make a thicker concoction yourself and pipe it around.

I'd echo boulangere. If it's not overly sweet already and can take some powdered sugar, the sugar should do the trick. But if you need to balance out the sweetness, some lemon zest and a drop of juice (assuming it's not a chocolate icing) , or cream cheese would do the trick. Also, try adding a touch of kosher salt if the sweetness becomes an issue. In the alternative, icing is really easy to make. You may want to simply start afresh. There should be recipes here or on marthastewart, epicurious, etc.

Add some powdered sugar, and maybe some room temp cream cheese.