Hitting specific color of orange in a sponge cake
You cannot just use random ingredients and have the cake "become" their color. Even if you used 100% carrot, the color would change during baking. So you really have to use a colorant. 

The best way to do it is to purchase a good quality ready-mixed colorant like the Wilton paste colors, and use the exact shade you want, in sufficient amounts. You will have to test it only on a few cakes (or maybe several cupcakes within the same batch) to find out what amount you need for the exact orange you want. 

If you want to match it from cheaper and more ubiquitous dyes which are available in few hues, you will have to work with color triangles to match. I won't go deep into that, but you will need about 66 samples per test round, and probably 2-3 rounds. Each sample can be a mini cupcake so you don't waste much material, but you will need exact measuring instruments and lots of patience. 

Many people have an instinctive negative reaction to that and want so stay "natural" in their colorant choosing. In principle, you can also try to use strong natural coloring instead of azo dyes, for example colorant based on anato or a mixture of turmeric and beetroot. The problem is that in sufficient amounts, they will give an undesired taste to your cake. Also, you will have more difficulty matching the color, since the colors you start with are not as pure or as saturated. So expect more than just 2-3 rounds of color triangle work. 

If you don't even accept plant matter which has industrially been turned to dye, and want to produce the pigment in your own kitchen, this will be very difficult to achieve at all, and much more fickle. Basically, the final color will most likely not be at all the shade you wanted it, it won't be colored through and through but will have specks of a solid throughout the dough, and it will have a strong taste of something not-cake-like. 

This all assumes you want to color the sponge of the cake itself. You can always achieve a celebratory cake by decoration. Mixing in Wilton colors into icing is much easier, because you can see what the final color is going to be right away, so you can always add color or icing until you match the shade (unlike the sponge where you add once and then wait for it to be baked to see the result). Or you can forget the coloring and just sprinkle candied orange peel or something similar to get a nice decoration which has the color you want.