Root phenotyping is particularly challenging because of complexity and inaccessibility of root apparatus. Orientation is one of the most important architectural traits of roots and its characterization is generally addressed using multiple approaches often based on overall measurements which are difficult to correlate to plant specific physiological aspects and its genetic features. Hence, a 3D image analysis approach, based on the recent method of Straumit, is proposed in this study to obtain a local mapping of root angles. Proposed method was applied here on radicles of carrot seedlings grown in real weightlessness on the International Space Station (ISS) and on Earth simulated weightlessness by clinorotation. A reference experiment in 1g static condition on Earth was also performed. Radicles were imaged by X-ray micro-CT and two novel root orientation traits were defined: the "root angle to sowing plane" (RASP) providing accurate angle distributions for each analysed radicle and the "root orientation changes" (ROC) number. The parameters of the RASP distributions and the ROC values did not exhibit any significant difference in orientation between radicles grown under clinorotation and on the ISS. Only a slight thickening in root corners was found in simulated vs real weightlessness. Such results showed that a simple uniaxial clinostat can be an affordable analog in experimental studies reckoning on weightless radicles growth. The proposed local orientation mapping approach can be extended also to different root systems providing a contribution in the challenging task of phenotyping complex and important plant structures such as roots.