In principle there's nothing stopping a plant from developing a natural radio.
Let's start with what a radio really is, in the most reductive form. A radio is nothing more than an antenna made of conductive material to particular dimensions, to make it resonant with electromagnetic waves of a particular frequency. By applying a changing electrical charge to it, we can cause it to emit signals of that frequency, and we can use it to receive signals of that frequency. Optionally, we might add a waveguide to concentrate or direct the signal.
The conductor is easy - any nervous system is already a network of conductors transmitting electrical signals. Forming a section of nerve-like tissue in the shape of a patch antenna (so named for simply being a rectangle of copper on a surface or similar), placed near the surface, would make a perfectly serviceable, if rudimentary antenna. With this alone the rocket could communicate by radio over short distances by thinking into the antenna. Power is an issue but not insurmountable, given your plant is intelligent and able to grow rockets.
Adding a waveguide isn't much harder. A properly shaped section of wood could easily act as a parabolic dish, and specially shaped cavities to act as resonators and waveguides is not without precedent- whales and dolphins already evolved this for their sonar. On the ground, a natural crater or dormant caldera would make for a marvellous dish - a particularly tall tree with a handful of antennae at the focal point of the dish would make for an excellent receiver.
Combining the two, you could in theory have a plant that manages to incorporate a radio. It doesn't have to be a patch and a parabolic dish, either: if your plant can engineer a rocket, it can engineer an antenna and waveguide of any kind.
In practice a lot will depend on the specific properties of the materials available to your plant. Mere wood as we know it is unlikely to be suitable for a waveguide, and the nervous system is unlikely to be up to the task of transmission. In the case of Avatar, the superconducting unobtanium rather dramatically solves the latter issue, though something more boring like a copper nervous system would probably be more than sufficient. Either way some exotic plant materials may be necessary to make this all work.