I don't recommend it. Anemones are largely made up of water, therefore they need stable, pristine water conditions in order to thrive. This usually doesn't happen in young tanks. Give your filtration time to build up beneficial bacteria to help maintain stability. Once your tank is more mature, there usually aren't fluctuations in parameters and this is when an anemone can do well, which is usually at the 6+ month mark of your tank.
Most anemones also need good lighting, this is another thing to consider.
What type of anemone are you looking at exactly? There are many anemones that are purple or have a purple variety.