Radiotherapy with narrow scanned carbon ion beams enables a highly accurate treatment of tumours while sparing the surrounding healthy tissue. Changes in the patient's geometry can alter the actual ion range in tissue and result in unfavourable changes in the dose distribution. Consequently, it is desired to verify the actual beam delivery within the patient. Real-time and non-invasive measurement methods are preferable. Currently, the only technically feasible method to monitor the delivered dose distribution within the patient is based on tissue activation measurements by means of positron emission tomography (PET). An alternative monitoring method based on tracking of prompt secondary ions leaving a patient irradiated with carbon ion beams has been previously suggested. It is expected to help in overcoming the limitations of the PET-based technique like physiological washout of the beam induced activity, low signal and to allow for real-time measurements. In this paper, measurements of secondary charged particle tracks around a head-sized homogeneous PMMA phantom irradiated with pencil-like carbon ion beams are presented. The investigated energies and beam widths are within the therapeutically used range. The aim of the study is to deduce properties of the primary beam from the distribution of the secondary charged particles. Experiments were performed at the Heidelberg Ion Beam Therapy Center, Germany. The directions of secondary charged particles emerging from the PMMA phantom were measured using an arrangement of two parallel pixelated silicon detectors (Timepix). The distribution of the registered particle tracks was analysed to deduce its dependence on clinically important beam parameters: beam range, width and position. Distinct dependencies of the secondary particle tracks on the properties of the primary carbon ion beam were observed. In the particular experimental set-up used, beam range differences of 1.3 mm were detectable. In addition, variations in the beam width could be measured with a precision of 0.9 mm. Furthermore, shifts of the lateral beam position could be monitored with a sub-millimetre precision. The presented investigations demonstrate experimentally that the non-invasive measurement and analysis of secondary ion distributions around head-sized homogeneous objects provide information on the actual beam delivery. Beam range, width and position could be monitored with a precision attractive for therapeutic situations.