Yes, you can file a claim for workers' comp and Social Security disability (SSD) benefits simultaneously. However, you'll be approved for Social Security disability benefits only if your impairment is severe and is expected to last a year or more, preventing you from doing any kind of substantial work.
While the two benefit systems are completely separate (SSD and SSI are standardized federal programs, while workers' compensation laws differ state to state), the Social Security Administration may lower your disability payments by the amount of your workers' compensation benefits, by taking what's called an "offset."
An individual seeking both types of benefits may gain advantage from the input of a workers' compensation attorney since timing issues regarding an SSD claim can, in some cases, affect a workers' comp claim. You might want to choose an attorney who can handle both types of claims, though very often, attorneys will handle only one or the other -- that is, either Social Security disability cases or workers' compensation cases. However, either type of attorney should be able to advise you on whether your disability benefits would be reduced by workers' comp benefits.