Can a reservist volunteer for deployment?

SPC (Join to see), Yes. There are numerous opportunities for deployment on the Tour of Duty Site located at https://mobcop.army.mil/. Additionally, your Local S1 should be able to find out for you if any are coming up throughout your command.

Tour of Duty (TOD) is an internet site where Reserve Component Soldiers (USAR, IRR, ARNG, IMA) can find and volunteer for active duty tours.
Any command that has positions or missions that could be filled by a RC Soldier can post those jobs on Tour of Duty. TOD allows commands to build and validate their positions so the vacancies can be searched by Soldiers seeking active duty. The positions in TOD must be validated by the command that owns the position or mission before they can be listed. Soldiers can find positions that match their grade and skills and then request the hiring command consider them for the job. If the Soldier does not see a current position they want to volunteer for, they can still post their interest in serving on active duty - the hiring commands will be able to see their name, grade and MOS in a pool of potential volunteers for future openings.
The hiring command will review the list of Soldiers interested in their positions and select the best qualified Soldier. Once selected, the Soldier must either accept or decline the position. If they accept, TOD transfers the active duty application (packet) to another internet site, where the Soldier electronically signs their voluntary request for active duty. Once submitted by the Soldier, the DAMPS-A packet is sent electronically to the Soldier's chain of command for review and release. If the Soldier is released, the packet is forwarded electronically to the HQDA approval system - DAMPS - for final review and approval. Approved packets are transferred to the command that issues the orders for the tour. The process usually takes 30-60 days to complete. To learn more, visit the TOD web site at https://mobcop.aoc.army.pentagon.mil and select "Tour of Duty" or Google "MOBCOP".

https://mobcop.aoc.army.pentagon.mil/

Sure, believe me there's always someone looking to get out their deployment obligation. However, it is the reality of the service and they always need other soldiers to cross level.