It might, but that's really not what you want to use one for. A CBD roll-on is a topical application that's intended for use on sore muscles, more for physical pain rather than having neurological symptoms.
The slightly less short version is that while CBD is known to have anti-anxiolytic properties (anti-anxiety) a roll-on doesn't deliver enough of it and also doesn't deliver it in a way that's beneficial when it comes to relieving anxiety.
So you're probably better off using something else, such as a CBD tincture.
Bear in mind that the science regarding CBD is still very new. The exact details of how it works on the body and all the different beneficial properties - as well as the negative - is not fully understood.
At the moment, medical science has something of an empirical understanding of the basics of how CBD works on anxiety and other conditions, meaning it's somewhat understood what CBD does, but the how and the why aren't.
So, what does it do? Bear in mind that this is the simplified version, of course!
Part of what creates anxiety - besides reactions to stimuli (meaning things that cause anxiety) of course - are a type of neurons called GABA A receptors. GABA A receptors monitor the levels of the neurotransmitter gamma-aminobutyric acid, or GABA.
GABA is an inhibitor, which you need a certain balance of for healthy brain activity. If you have too little of it in your system, the brain tries to compensate for its absence and that creates the emotional state of anxiety.
You might have heard of a class of drugs called benzodiazepines. These include commonly-prescribed drugs such as Mogadon, Ativan, Valium and Xanax.
How they work is by modulating how the GABA A receptors work, essentially recalibrating the GABA A receptors. What's been observed is that CBD has a similar effect; it works on GABA A receptors in a similar fashion and therefore reduces anxiety.
That sounds like a lot, doesn't it? Okay, so how does a CBD roll-on and/or tinctures come into the picture?
One of the things to know about CBD roll-ons is that they provide a rather low dose of CBD relative to other CBD products per application.
While the container as a whole may have upward of 200 mg of CBD, every topical application of - say - a 3 oz container is only going to have a few milligrams.
Compare that to, say, a 1 oz bottle of 1000 mg CBD tincture. Every dropper-full contains upward of 40 mg of CBD. That's a lot more.
Another thing to bear in mind is how well the CBD itself is actually absorbed.
The CBD from a roll-on is absorbed through the skin, meaning it has to pass through the skin, the small veins and blood vessels of the skin and down into the muscles, and eventually into the bloodstream.
By comparison, taking CBD oil under the tongue only puts a paper-thin layer of skin between the tincture and the bloodstream.
The point here is that a different type of product, such as CBD oil, gives you far more CBD oil per dosage and more of it gets absorbed into the bloodstream and therefore gets into the body.
If you have a condition that you want to take CBD for that isn't related to the muscles or the joints, a CBD tincture is a far better choice of product to try and alleviate it with. Chronic pain, anxiety and other mental disorders require CBD to act on the brain.
And for lasting relief, you need more of it in your system.
Since a roll-on gives you a low dosage per usage, and since it isn't absorbed as efficiently, it's really not the product for trying to ameliorate anxiety, whether acute or chronic. A tincture or capsule is a far better tool for the task.