Even though you may not have seen this before, but the string will not necessarily always behave the same.
If it is just the string and the liquid then you will get an effect called the Cheerios effect (Am. J. Phys. 73, 817 (2005)) that causes the string to clot. This is caused by the string locally deforming the surface due to a balance of buoyancy and wetting adhesion, which causes the surface energy to go up. Minimization of the surface energy drives the string to clot together such that it deforms the surface as little as possible.
Note that this clotting will only occur if the energy gain for by clotting is not balanced by an energetic contribution for the bending of the string i.e. if it would be a rubber like material it will probably not (fully) clot, but with a normal piece of cotton string I think it will.
A nice circular loop can form if Marangoni effects play as suggested by Mark Rovetta. In this case adding a detergent or a bit of oil inside the string will cause the surface tension to lower such that it is energetically favorable to create more surface area with this low surface tension, causing the liquid with oil/detergent to flow outwards and open up the string into a loop.
I have explained this in terms of energies (because that is so much easier when thinking about surface tension effects), but to answer the part of your question on the direction of the force: it acts perpendicular to thread because that is the direction of the energy gradient when clotting or expanding. The tension in the thread itself is indeed parallel to the thread as explanation by Mark.
Footnote: I just found out that this question is strongly related to Why does a cork float to the side of a glass?, in particular the answer by Pulsar is useful in this context.