  Mixed $^3$He-$^4$He droplets created by hydrodynamic instability of a
cryogenic fluid-jet may acquire angular momentum during their passage through
the nozzle of the experimental apparatus. These free-standing droplets cool
down to very low temperatures undergoing isotopic segregation, developing a
nearly pure $^3$He crust surrounding a very $^4$He-rich superfluid core. Here,
the stability and appearance of rotating mixed helium droplets are investigated
using Density Functional Theory for an isotopic composition that highlights,
with some marked exceptions related to the existence of the superfluid inner
core, the analogies with viscous rotating droplets.
