Do short term disability payments from an employer disability insurance plan count towards the social security annual income limit

Hi. By 'annual income limit', I assume that you're referring to Social Security's earnings test (https://www.ssa.gov/benefits/retirement/planner/whileworking.html). In that case, the answer to your question is no. Any type of insurance payment that is not subject to payroll taxes would not count as earnings for purposes of Social Security's earnings test.

Best, Jerry