A turboprop plane can be pressurized in the same way a turbofan plane can: via bleed air from the compressor stage of the turbine engine. A turboprop and turbofan are not that different actually. You have a turbine engine core that powers the big fan at the front or the big propeller via a gearbox (although the turbofan still gets some of its thrust from the engine core, but the turboprop does not):
(image source)
On the Dash-8 Q400 for example, the engines provide bleed air for pressurization:
The aeroplane is pressurized by engine bleed air supplied to and distributed by the air-conditioning system. Pressure is maintained and controlled by the cabin pressure control system which governs the rate of
outflow from the pressurized areas (Figure 12.2-10) of the aeroplane. An aft outflow valve primarly
controls the outflow of air, and is assisted by two safety valves.
(Dash-8 Q400 FCOM - Air Conditioning and Pressurization 12.2.2.1)
Air entering at the engine inlet is directed rearard and compressed (Figure 12.23-1). Two
compressors carry out compression for combustion and bleed extraction purposes. Air is first ducted
to the low-pressure (NL) axial compressor and then to the high pressure (NH) centrifical compressor
where it undergoes a seconds stage of compression.
(Dash-8 Q400 FCOM - Power Plant 12.23.3.1)
The following image shows the bleed port in the PW150A engine as used on the Dash-8 Q400:
(image source)