You can do one for AC, using phase shift control, usually using a bridge rectifer so you can control both positive and negative peaks. DC is more of a problem, as you need some way of turning the SCR off - on AC it turns off automatically as the voltage drops to zero.
It doesn't seem a very good choice for a voltage regulator, what is he wanting to control?.
SCR will be fine with firing angle control. That way by changing the firing angle of the tyristors you can change the average DC link value (you will need a decent cap tho).
And since you are controlling on the AC side it is natually commutated so the Tyristor automatically turn off (as long as you remove the gating pulse)