The CDC recently issued updated face covering guidance to provide that a cloth face covering also offers some protection to wearer.
How well it protects the wearer from breathing in the virus likely depends on the fabrics used and how the face covering is made (e.g. the type of fabric, the number of layers of fabric, how well the mask fits). The CDC is currently studying these factors.
The CDC continues to emphasize the main function of wearing a face covering is to protect others, in case of asymptomatic infection.