It is not showing that it is for lease in the MLS, however, that may not be the case. But for a 1 bedroom 1 bath unit to be for rent for $800.00 per month in Santa Monica is very unlikely and the is probably a SCAM. Units in that building have rented for $1600 and above.
It is always a good thing for you to check out any and all rentals that you are interested in to make sure they are not SCAMS. There are many posted on Trulia, Zillow, Craigslist and other web sites where anyone can post.
Good luck with your search!
All the best,