Joint-manager Jon Boardman has described Williams as a "strong natural defender who loves defending".
Formerly with Cheltenham Town, Bishops Cleeve and Gloucester City, Williams also has an eye for goal, recording a number of goals already for Evesham United in the Evo-Stik League South West this season.
Boardman watched Williams play as part of a three-man defence in the Buildbase FA Trophy 3-1 defeat to Cirencester Town a month or so ago and was impressed with what he saw.
Striker Luke Hopper and former player Bradley Gray have also rated Williams highly and recommended the signing.