Of course it is possible! All the functions needed for the calculations are available on a scientific calculator, e.g. square root, log, value for pi, etc.
The Wikipedia page should get you started.
Mark Glickman's page on the system should take you further.
This pdf has detailed descriptions and equations for Glicko-2 - http://www.glicko.net/glicko/glicko2.pdf.
I've edited the question to make my implication clear: is it feasible to calculate the Glicko rating with the assistance of a scientific calculator?
Back in 1983 when I was working on the lateral guidance team for the flight management and control system for the Airbus A310 I used 2 programmable calculators, the HP15C and the HP16C to generate test data. These Glicko algorithms could be programmed into those calculators using 38 year old technology. I don't know what calculator you have nor what your programming skills are but for a competent programmer with a reasonably good 20th century programmable calculator it should be straightforward.