It looks like Purple Heart plant (Setcreasea pallida
'Purpurea'), also known as Tradescantia pallida
'Purpurea'. It's often grown in warm climates as a ground cover. It's one of several plants known by the common name of "Wandering Jew".
It should root easily in water, or just about any moistened growing medium, such as potting mix, sand, or perlite. To root, I recommend that you remove the leaves at the lowest node on the cutting and make sure that node is submerged in the water or buried in whatever medium you choose.
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams