It depends what the cause of your anxiety is. It's possible a lack of certain vitamins/minerals could be the cause of your issues and a healthier diet might resolve that.
But I think in most cases it's a flaw in our thinking and diet won't magically change anything in that sense. Though it will help!
Over the past few months I've taken on a healthier lifestyle. Very little to no pop, alcohol (though I never really drank much to begin with), sugar, sodium and I mostly eat veggies, fruit, fermented dairy products and nuts. It helps in that you feel more confident because you feel healthier and stronger and have more energy and it feels good to be supplying your body with what it needs rather than feeling guilty eating a box of doughnuts all by yourself :|. If you were eating very poorly before, you might also notice a change in your teeth, skin, hair and weight, which would also give you a bit more confidence to work with.
It's certainly not going to harm you anyway.
Worth a shot!