Is it possible to set a tower shield in a place to gain cover but without the the need to hold it with one arm?
No, you cannot
There are no feats or archetype abilities that allow you to gain the benefits of a tower shield without actually holding it. All abilities that allow you to gain AC/cover benefits from a tower shield require you to be holding it.
But you can benefit from it if it's animated
Animated tower shields can be "dropped" and still provide all of its bonuses to its owner:
As a move action, an animated shield can be loosed to defend its wielder on its own. For the following 4 rounds, the shield grants its bonus to the one who loosed it and then drops. While animated, the shield provides its shield bonus and the bonuses from all of the other shield special abilities it possesses
There are also other magic items that have similar behavior, such as the Battlement Shield:
Once per day on command, this +2 tower shield can transform into a solid, 1-foot-thick, 10-foot-by-10-foot wall of masonry with a battlement on top and an arrow slit in each 5-foot length. The wall acts as cover just like any physical wall.
Or Fortress Shield:
The wearer of this +1 tower shield may, as a full-round action, transform the shield into a 1-inch-thick cube of iron that springs into being around him, completely enclosing his space.