You can try it, but I don't recommend it! I have yet to see any research showing that charcoal will whiten stained teeth. It may remove some yellow surface stain from plaque and calculus, or even tobacco tar, but for most folks it's not going to get you the results you want. I think if anything it might seem like your teeth are whiter simply due to the contrast of the black color of the charcoal. Be careful too, typically charcoal is abrasive and can damage your enamel.
Professional Teeth Whitening in Missoula
You're much better of have a custom set of bleaching (AKA whitening) trays made at our office, or even using over the counter whitening products like Crest Whitestrips to get a brighter, whiter smile.