Adding a bit of red to a lot of yellow will give "orange." If you add a saturated color like red in the same proportion as a "light" color like yellow, you'll completely overwhelm the yellow.
The proportions can be changed just a bit though to give different oranges from red-orange to marigold.
If you want to make it more of a "toned-down" orange kind of on the way to rust, etc, you can add brown, or make brown first by mixing red+green then add that, or just add a tiny tad of green or even blue.
Adding orange juice would be way too diluted and weak to change the color very much. Concentrated oj would work better, but food colorings are very concentrated colorants.