From A Glossary: Or, Collection of Words, Phrases, Names, and Allusions to Customs, Proverbs, &c., which Have Been Thought to Require Illustration, in the Works of English Authors, Particularly Shakespeare, and His Contemporaries by Robert Nares, page 248:
TO FACE IT WITH A CARD OF TEN. A common phrase, which we may suppose to have been derived from some game, (possibly primero), wherein the standing boldly upon a ten was often successful. A CARD OF TEN meant a tenth card, a ten.
Also similar from The Dramatic Works of Ben Jonson: Printed from the Text by Ben Jonson, Peter Walley:
A card o' ten, is what we now call a tenth card, and the phrase "to face it with a card of ten," is to win it, or get the better of it. To this purpose Shakespeare:
Tra. " A vengeance on your crafty wither'd hide !
" Yet I have fac'd it with a card of ten." Taming of the Shrew.
Which passage Mr. Warburton thus explains, that is, with the highest card, in the old simple game of our ancestors; so that this became a proverbial expression.
The suggestion that "ten" was the highest card can be found in Wikipedia, under the English version section of Primero:
Each player receives 4 cards dealt in 2’s from a 40-card deck ranking K Q J 7 6 5 4 3 2 A.