If you do a clean installation of Microsoft Office and Microsoft Office Visio, the WordArt command does not appear on the Picture shortcut menu on the Insert menu. A clean installation means that you do not upgrade from an earlier version of the program.
If you upgrade to Office and Visio, you may see the WordArt command when you first start Visio, but the WordArt command is unavailable (appears dimmed). After you open a template or a blank drawing, the WordArt command no longer appears on the menu.
This behavior is by design.
There is no WordArt gallery in Visio. (A WordArt gallery is required for the WordArt feature to work.) Additionally, Visio cannot use Word Art galleries from other Office programs. Therefore, there is no WordArt functionality in Visio.