Maybe. Although not my first choice as a natural remedy for anxiety, ginsenosides (one of the components of ginseg) may have anxiety-reducing properties. Depending on the type of anxiety, theanine and kava are two alternatives to consider for anxiety.
Don't waste your $. There is no systematic evidence that ginseng helps anything, including anxiety. Ginseng is one of those bogus "ancient wisdom" things. Its use is based on a SUPERSTITION called the "doctrine of signatures:" because the root looks like a little headless man, the ancients got this delusion that it would cure things. (Wrong.) Be skeptical. Arm yourself with modern knowledge, not ancient superstition.
Ginseng and anxiety. It can. Ginseng can reduce levels of stress in both men and women. It can increases a sense of well being and stamina, and has been used to help with erectile dysfunction and symptoms relating to menopause. All of these effects may help calm the mind and be beneficial for anxiety.