We present the first steps to develop radiation sensors based on the graphene field effect transistor technology. Such a sensor exploits the ambipolar behavior of graphene near its Dirac point and it is not dependent on collecting charges, but it senses ionizing radiation trough the change in conductivity of the graphene layer induced by changes of the electric field. We designed the layout of the sensors with the help of Sentaurs TCAD. We simulated static operations and the dynamic response to radiation and calculated the source- drain current through the graphene layer with a quasi-analytical model. The transistors were produced at the National Enterprise for nanoScience and nanoTechnology by depositing high quality graphene on silicon chips manufactured by the Fondazione Bruno Kessler foundry. To reduce the high contact resistance between graphene and aluminum contacts caused by oxidation of the aluminum surface, we used gold/chromium interfaces. We investigated the sensors behavior by mean of electrical measurements, extracting the graphene properties, such as mobility and doping. We observed modulation of the source-drain current, determined the Dirac point and found the optimal voltage levels to be sensitive to pulsed IR laser light and beta-particles.