First of all, the question here falls entirely within the scope of classical electrodynamics, so that's the framework in which to look upon this answer.
First of all, electric *current* is the MOTION of charges, mainly electrons in metallic wires.
Radiowaves are dynamical configurations of the electric and magnetic fields in free space (or in air) which tend to propagate through space at the speed of light. In fact, the dynamical configuration corresponds to a continuing alternation between electric fields and magnetic fields. In the case that the frequency of this alternation is below a certain limit, one calls this phenomenon a radiowave. If the alternation is faster, we give it different names, such as, microwaves, infrared radiation, visible light, UV light, X-rays, ... because the physical phenomena affected by it change in nature.
Now, what's the link between electric current and radiowaves ? Well, both are linked. An alternating electric current can generate a radiowave of the same frequency, and vice versa: a radiowave hitting a conductor can generate an alternating current in the conductor.
But they are not the same phenomena !
How do you make an electric current ? Simple: "pump" charges through a closed circuit of conductors. The "pump" can be a battery, a generator, you, with a small tool picking up electrons and pushing them into a wire (matter of speaking of course

)...
How do you make an alternating current ? Well, force the current one way, then the other way, then again one way, ... with switches, or transistors, or any other technique.
With your conductor in which flows an alternating current, you can make radiowaves (of the same frequency). Simply put a line of conductor somewhere (straight, or in a loop...). It will generate some radiowaves, which will then propagate freely throughout the air and the vacuum, into space. Once they "leave" the wire, they propagate freely on their own.
When you slow down the frequency of an alternating current, you
generate less and less strong radiowaves with a given conductor in which your current flows. And when you stop the current alternation all together, and have a DC current, you do NOT generate a radiowave anymore. What you now generate is a (weak) magnetic field, "attached" to the wire, and which won't propagate. At least, when you turn your current SLOWLY on and off, because switching the current, itself, contains an AC part which WILL generate a radiowave.
cheers,
Patrick.