That is not easy to answer because it can be difficult to agree on what is meant by "reaction time" of the brain. If you're thinking of the time between receiving a stimulus (e.g. a flash of light) and a major physical response (e.g., stepping on the brakes), the time really depends on the length of the signal chain from the retina of your eye to the activation of your leg muscles. That tends to be around 0.275 second.
To quote from Sourakov (2009):
The fastest tactile reflex time belongs to the star-nosed mole, Condylura cristata L., which uses 22 nasal appendages to navigate through soil and can react in just 120 ms, when one of these appendages comes in contact with food (Catania & Remple 2004). Here, I would like to report the startle reflex time in skipper butterflies, which is among the fastest recorded for the animal kingdom and which is at least twice as fast as startle eye-blink reflex of humans.
Startle reflexes have evolved as fast defensive (usually escape) responses in animals, engaging subcortical reflex mechanism that bypasses cerebral processing and voluntary movement. Because circuits involved are shorter, the latencies of the startle reactions are much shorter than those of voluntary reactions. In terms of electromyographic responses recorded in vitro, acoustic startle reflexes tend to be very short. In rats, for example, electromyographic responses can be as fast as 5–10 ms, and in humans as fast as 14 ms (Yeomans & Frankland 1995).
So the method of measuring reaction time has a strong influence on results, because it can amount to measuring reaction at different points in the signal chain.
Finally, it has been shown that task complexity, level of mental arousal, and conditioning can all affect reaction times. One hypothesis is that those influences can change the effective length of the signal chain going from stimulus to response. Drugs can affect any of several factors that contribute to the length of the signal path and the speed at which a signal propagates along the signal path.