Can anxiety give you brain fog?

Yes, brain fog's biggest cause is stress, it is however, a symptom more than a condition on its own. Stress, anxiety and poor diet contribute to it, and its essentially the same principle as a computer, using up a lot of background memory making everything run slowly. An easy way to clear it is exercise and moments of peace to try give your brain time to rest. Sit alone with your thoughts for a bit and just try to clear your mind. Barring that, diet, exercise, reducing electronics use and no smoking or alcohol.