A union card is also called a “showing of interest.” It’s essentially voting with your signature that you want to form a union with your co-workers. Union cards are available either as paper cards or electronic forms and ask for personal information (like name, job title, email address). The legal language is “I authorize the Writers Guild of America, East as my collective bargaining representative.” That means that you want to form a union with your co-workers and you want that union to be part of the Writers Guild of America, East.
Union cards are kept with WGAE staff - names and information of card signers are not shared with management.