A linear cryogenic 16-pole wire ion trap has been developed and constructed for cryogenic ion spectroscopy at temperatures below 4 K. The trap is temperature-variable, can be operated with different buffer gases, and offers large optical access perpendicular to the ion beam direction. The housing geometry enables temperature measurement during radio frequency operation. The effective trapping potential of the wire-based radio frequency trap is described and compared to conventional multipole ion trap designs. Furthermore, time-of-flight mass spectra of multiple helium tagged protonated glycine ions that are extracted from the trap are presented, which prove very low ion temperatures and suitable conditions for sensitive spectroscopy.