Yes taking vitamins can cause anxiety in some people.
A common side effect of taking vitamins for some people is anxiety and if you already suffer from anxiety the vitamin intake can increase your anxiety especially if you take the vitamins long term.
However not everyone will experience anxiety from taking vitamins but it's normal for some people to get anxiety from vitamins and vitamin supplements.
Vitamins and those that contain copper, manganese and selenium are stimulating and can lead to anxiety and if you do have an increase in anxiety or have suddenly started getting anxiety when taking vitamin supplements then you should speak with your doctor about it.
Although the increase in anxiety is not all that serious but it's still good to speak with your doctor as they can recommend some solutions to hopefully decrease the anxiety.