A vernier protractor can do this: https://uk.rs-online.com/web/p/protractors/2357550/?cm_mmc=UK-PLA-DS3A--google--CSS_UK_EN_Hand_Tools_Whoop--Protractors_Whoop--2357550&matchtype=&aud-842313741538:pla-297036287733&gclid=CjwKCAjw1JeJBhB9EiwAV612y3g4Ug0JA5Q0kGyEdcM05mYdyJTUmLTz-J_Si6J3H21hjRj5ypZ86hoCXlkQAvD_BwE&gclsrc=aw.ds
The digital equivalent would use a high precision rotary encoder (they are available upto millions of counts per revolution!).
MEMS accelerometers are not accurate enough for what you want.