First of all, by the time Alpha Centauri A becomes a red giant, it will no longer be this close to the Sun so it probably wouldn't be visible. But let's assume it does stay 4.2 ly away.

By the Stefan-Boltzmann Law, the luminosity of a star is given by 

$$L = 4\pi R^2 \sigma T^4$$

Assuming a radius of $200 R_\odot$ and a temperature of $3600 \text{ K}$, we get a luminosity of about $6021 L_\odot$, compared to a present-day luminosity of $1.5 L_\odot$.

This means that the red giant would be 4014 times brighter, corresponding to an apparent magnitude increase of 9 magnitudes to about -9 apparent magnitude. This is slightly dimmer than the brightness of the moon.