Yes experiencing psychological stress or high anxiety can cause muscle jerks and muscle twitching which is normal.
If the muscle jerks and muscle twitching are only happening when you have anxiety then it's normal and usually nothing to worry about.
But if the muscle jerks or muscle twitching are happening when you're not having anxiety attacks etc then it could be something more serious that is causing it.
High anxiety levels can lead to muscle tension which then leads to muscle jerks which are normal and should go away once your anxiety calms down.