Inori offers Shu the Guilty Crown(a form of the Cat's Cradle) in the first episode. Is the Cat's Cradle variant Jacob's Ladder?
Yes, the string figure Inori offers is 4-step Jacob's Ladder.
In Japan, the hobby is known as ayatori. Also, in ayatori term, the string figure Inori offers is called hashigo (ladder), specifically 4-dan hashigo (4-step ladders).
From Xspy70's post about "Guilty Crown Ending Explanation/Interpretation" on MyAnimeList Forums,
The shape that Inori and Mana present to Shu in the beginning of the anime using strings is called Jacob's Ladder. It represents the staircase to heaven according to the book of Genesis. By asking Shu to take it, they imply that he should accept the (guilty) crown and be the king of the new world. In the end however, Inori, using the life strings, gives him a shape of an open eye (or Cat's Eye, from a string game called Cat's Cradle). When Shu takes it, the eye shape "closes" (Fish in a Dish string figure). Aside from being a foreshadowing of the rest of his life, a closed eye also means he is relieved from his unwanted duty of being the king. Closed eye (which also means blind) also means innocence. The Innocence that Shu was striving for for so long. It was his redemption from the responsibilities he never wanted to take. It meant he no longer had to be the king. It meant that he should no longer be "guilty."