In recent years, much attention has been paid to the characterization and creation of new bioinks, as it is believed that this is one of the main reasons for the slowdown in the development of the 3D bioprinting field. Therefore, the purpose of this study is to evaluate the possibility of using essential oils as bioinks of plant origin. To create scaffolds, a Coolness 3D printer (IPC&C, Ukraine) was used, and an infusion pump was used as a dosing system for bioink. The 3D print models were created using FreeCAD software. All STL-files were prepared for printing using the free Cura slicing software, with layer thicknesses of 450 μm to generate G-code for 3D printer. The printing process was controlled using the open source Pronterface software package. The essential oil of Oríganum vulgare, obtained by extraction with liquefied gases, was used as bioink. Printing was carried out in a hydrophilic support gel consisting of 1.2% Carbopol 940 and 0.04% bromothymol blue. To increase the viscosity of Carbopol 940, a 10 M NaOH solution was used. The shape fidelity and characterization of filaments of the 3D scaffolds were evaluated according to the protocol described by Schwab et al. (2020). Three-dimensional constructions were obtained printed with the essential oil of Oríganum vulgáre in the hydrophilic gel. In all the cases studied, the obtained filaments were heterogeneous. During the study, it was found that an extruder with a hole diameter of 0.583 ± 0.05 mm is most suitable for printing with essential oil. When printing structures with an extruder with this hole, a decrease in an uneven index of printing along all the axes under study is observed. Thus, the uneven index of printing along the Z axis was 123.8%, while an increase in the diameter of the extruder hole by 2.4 times leads to a proportional increase in the unevenness parameter. Reducing the extruder diameter below 0.583 results in uneven extrusion of the bioink. We have shown that the optimal bioink extrusion speed is 100 mm/s, while the printing unevenness along the X, Y, Z axes is 94.66%, 96.47%, and 123.48, respectively. For all printed structures, the value of the pore printability coefficient lies in the range from 0.92 to 1.00, which in turn indicates a good geometry of the printed pores. The conducted research indicates the possibility of using Oríganum vulgare essential oil as a bioink for 3D printing in a hydrophilic support gel.