A magnetic spectrometer determines the signed rigidity of charged particles by measuring their trajectories in the presence of a magnetic field. High Temperature Superconducting (HTS) magnets can operate in space without the use of a cryogenic liquid. While HTS magnets have many potential applications in space, including active magnetic radiation shielding, we present the design of an HTS magnetic spectrometer with a toroidal magnet providing a bending strength of 3 T m. The toroidal magnet is about 2 m in outer diameter, 2 m in height, and requires about 60 km of 12 mm wide ReBCO HTS tape. The magnet operates with an engineering current density of 855 A/mm² at a temperature of 20 K and a peak magnetic flux density of about 12 T. In the context of the HTS Demonstrator Magnet for Space (HDMS) project, we have designed and are building a small-scale coil pack of the toroidal magnet. The demonstrator magnet consists of two racetrack-like coils enclosed with copper bands that function as current leads and layer jumps. The no-insulation winding method facilitates self-protection against quenches. A lightweight mechanical structure made from aluminum alloy supports the coils.