Technology is sort of there, nuclear pulse propulsion or molten salt rocket (supercritical nuclear fluid) can do 20-30% speed of light with existing designs. And don't forget that time dilation makes the trip shorter for passengers, if we can reach 40-50% the speed of light it starts to make the trip a lot more reasonable.

A nuclear pulse rocket might be able to have constant acceleration for the whole trip which can help with artificial gravity too.

The big problem at those speeds is shielding, high energy radiation and high energy particles. Not a prohibitive challenge however.