Can you transfer soil plant to hyrdoponics?

Sure you can!

All you need to do is remove the plant from the ground with as much of the roots intact as possible (which is easier to do with potted plants than those planted in the ground). Then very carefully wash the root ball, gently removing the dirt. You want to remove absolutely all of the dirt if possible, but close is good enough. Better to err on the side of not damaging the roots than getting all the dirt.

Once that's done you just transplant it into the hydroponic system and start it up.

Sometimes, it's a good idea to keep the plant isolated for a period (quarantine), for example, not introducing it into a system that contains healthy, established hydroponic plants for a week or so. Even small particles of soil may harbour pathogens that we not harmful to the plant in soil, however, they could be infectious and spread rapidly in re-circulating hydroponics systems. Inoculating valued plants with beneficial microbial products (for example, containing "trichoderma")that colonize the growing medium and plants roots will not only help to prevent diseases; it can also improve growth rates and yields.

Keep in mind that like any transplantation your plant will experience stress and shock, and likely look very sick for a few days or even a couple weeks. Focus your attention on the newest growth since that's where the plant will be focusing most of it's survival efforts. It's a pretty big change for a plant grown in soil to find itself suddenly in a hydroponic system so the success rate is likely to be less than 100% especially for a beginner hydroponicist.

A product that adds vitamin B to the solution will reduce stress and help the plant transition more smoothly. I've used B-52 and Organic-B on different occasions for this purpose and they helped immensely.