Having a square business card does not outdate the traditional rectangular cards. They have their own significance. Rectangular shaped cards may be the old fashioned but there is a lot you can do with them to make them appear trendier. Change the layout of these cards by using better fonts and good material and they will look as modern as square shaped cards.
Have a look at these Square business cards and be inspired. These business cards were created and designed by professional designers.
Creative Square Business Cards
Chad Franz Business Card