It works. Here is my code if someone would ever be interested
$scope.uploadFile = function(fileName) {
if (document.getElementById(fileName).files[0] && document.getElementById(fileName).files[0].size > 0) {
var formData = new FormData();
formData.append('data', document.getElementById(fileName).files[0]);
formData.append('valueType', 'File');
$http.post('/engine-rest/task/' + $scope.camForm.taskId + '/variables/'+ fileName +'/data', formData, {transformRequest: angular.identity, headers: {'Content-Type': undefined}});
}
};