One of the most common reasons the leaves of a Geranium plant curl is because of an aphid infestation. Aphids dehydrate the plant and make any new and existing growth twist and turn into something that looks far from a healthy geranium plant.
Even though aphids are one of the most common bugs that infest houseplants, they can be controlled. A crucial thing to focus on when eliminating a bug infestation is following a routine plan of maintaining healthy plant life. This more than likely will include some sort of insecticide, but is not solely limited to having control through chemicals. Many people find natural solutions to coping with aphid infestations.
Some of these solutions are as simple as washing the plant with enough of spray to blow the little critters away. Another common natural alternative to insecticides is the use of neem oil. This oil is applied to the plants and provides a natural barrier to protect the plant from the aphids. Regardless of whether or not you decide to use insecticides or natural alternatives, getting rid of the hardly visible aphids is paramount to getting the geranium's leaves to grow properly without curling. Be sure to nurse the dehydrated geranium back to care with close attention to its watering needs.