Of course you can. There's nobody forcing you unless you are subject to a court order to take it. So assuming that's not the case, medication is entirely up to you. I'm guessing therefore that what you mean is, can one live with anxiety without taking medication or alternatively are there other ways of treating anxiety than medication. The answer to both is yes, but that doesn't mean that will work for you. Medication doesn't ever cure anxiety, it just makes it easier to live with. The first consideration is how severe your problem is. If you're able to function okay but want a better life, you don't need medication. Therapy should work for you, although it may take a while to find a therapist you click with and who specializes in treating anxiety. These days the type of therapy most recommended is some form of CBT, but any one that works for you is the one that works. Therapy takes time and a lot of work, but if it does lead you to stop thinking like an anxious person you will be cured, not just have your symptoms tamped down. Another approach is to change your lifestyle and use natural medicine. This would involve changing your life pretty significantly most likely, but again, if this works you are also cured, not just medicated. Doesn't mean the problem will never return, but it does mean that some people are able through changing their diet, meditating, doing some therapy work, and using natural remedies you get back into balance and the imbalance that created the problem is gone. Sometimes as well anxiety comes for awhile and then just goes away as mysteriously as it appeared in the first place. Wouldn't want to bank on this happening, but it does fairly frequently. Now, if your anxiety is so severe you can't function then it's highly unlikely you have time for these things to work, as they do take time. Medication kicks in more quickly. If you're already on medication, stopping it has to be done with great care to prevent withdrawal symptoms and potentially getting a worse problem, so if you're aiming to try something else make sure you discuss with your psychiatrist and make sure your psychiatrist knows well how to handle the stopping process. Don't quit abruptly. So the answer is yes you can but that doesn't mean yes you will. Peace.
There are natural things you can do for anxiety. Lifestyle things, if you will. Good diet, exercise, proper sleep. Also, meditation, prayer if you are into that, leisure activities that are calming, deep breathing, having a support circle in your life, journaling, etc. Psychotherapy or talk therapy can be amazing if you have the right therapist who you connect with and knows what they are doing. In fact, I'd try these things BEFORE medication to see if they work. If they don't, adding medication an be beneficial for some.