You were close with $routeParams. If you use ui-router use $stateParams instead.
This code works for me:
.state('recipes.category', {
url: '/:cat',
templateUrl: '/partials/recipes.category.html',
controller: 'RecipesCategoryCtrl',
resolve: {
category: ['$http','$stateParams', function($http, $stateParams) {
return $http.get('/recipes/' + $stateParams.cat)
.then(function(data) { return data.data; });
}]
}
})