The crucial point is that to get to (low) relativistic speeds, you also need a relativistic exhaust velocity or the reaction mass just becomes untenable. Current ion thrusters are not up to the job.
For example, if you had a vehicle weighing 10t empty (but including energy), and a thruster capable of accelerating ions to 1% the speed of light, you'll only need 17t of reaction mass to achieve a speed delta of 1% the speed of light.
This ratio holds up as you scale exhaust velocity and delta V, so the exact same reaction mass would be needed for a 10% light speed delta V using a thruster shooting ions at 10% c. As a rule of thumb, you always need a reaction mass about 170% of the vehicle's dry mass when your thruster exactly matches your target velocity.
Now, to illustrate how critical exhaust velocity is, imagine you make thrusters with exhaust velocities 10x that of the target delta V. In those cases, you'll only need a reaction mass of roughly 10%. However, if your exhaust velocity is 0.1x the target delta V, you'll need a 2200000% reaction mass!
