"In the turtle boats I was in the cross-trees of the mast-head"

Public DomainCross-trees
Santiago is referring to his time on boats that hunted turtles.

The mast-head is simply the top of a mast on a sailing ship. Cross-trees, according to thefreedictionary.com, are "pieces of timber at a masthead, to which are attached the upper shrouds. At the head of lower masts in large vessels, they support a semicircular platform called the 'top.'"