Assumption: User is traversing issues as per How to traverse Issues in Backlog or How to traverse and rank issues in Sprint Board and user is now at issue link

Step 1: Press Control + M to open a dialog to update the rank.  Jaws will read the Sprint/Backlog default selected value.

Step 2: Make sure you are in forms mode by pressing Enter key and hearing the beep, which will basically expand the options of the Combo Box. Then press Down / Up arrow keys to select the Sprint or Backlog where you want to move the issue. JAWS will keep reading the selections as you press the Down/Up keys. To apply the selection that JAWS just read,  press Enter after that selection is read. Press Tab and Enter the numeric value of Rank

Step 3: Press Tab, JAWS will read Save button. Press Enter