Yes, beta blockers such as propanolol can help with stage fright. When you are performing in front of an audience and you have stage fright, what happens is that you have a fear of embarrassing yourself or you have a fear that the audience will make fun of you. So your fear triggers the sympathetic nervous system and triggers the release of adrenaline into the bloodstream, in a response called the fight or flight response. So your sympathetic nervous system uses epinephrine (adrenaline) as its neurotransmitter to signal the heart to beat faster, for instance. In addition, epinephrine (adrenaline) is released into the bloodstream from the adrenal glands, and this adrenaline then travels to the heart, so it can beat faster, for instance.
How beta blockers like propanolol work for stage fright is that the beta blocker blocks the adrenaline receptors. So in the case of the heart, blocking the adrenaline receptors prevents adrenaline from increasing the heart rate. Beta blockers also block adrenaline's effect in other organs, so that you don't sweat, don't breathe as fast, don't have a shaky voice, don't have trembling knees, and don't have butterflies in the stomach. So beta blockers prevent the physical symptoms of anxiety by blocking the adrenaline receptors.