The 29 workers are employed by Altrad-Hertel at the power station.
Union Unite claims the company is refusing to register the scaffolders under the National Agreement for the Electrical Construction Industry (NAECI).
Now Unite has called two 24 hour strikes starting next month when workers plan to picket all entrances to the power station site.
Unite regional officer Chris Weldon said: “The strikes are set to cause a great deal of disruption at Drax.
“The vast majority of construction workers at Drax work under the auspices of the NAECI agreement and there is no good reason why scaffolders should be treated any differently.
“Our members feel very strongly about this issue and they have voted for strike action as a last resort.
“Even though strike action has been announced it is not too late for the dispute to be resolved.
“Altrad-Hertel simply needs to enter into negotiations and agree to employ the scaffolders under the NAECI agreement.”