Sadly, string theory [or more properly superstring theory] is neither currently experimentally testable nor in a state of development where we can foresee it being so in future. When I was in graduate school, prospective doctoral students in the department [physics] were required to attend a seminar on the various research specialties of the various groups in the department. In physics at least, doctoral studies are treated as on the job training in doing professional research. When the speaker for the string theory group came I asked him the question, "What would it take to disprove superstring theory?" to which the reply was, "That is one of the biggest sources of criticism of string theory by physicists; we just don't know." Although I did not end up working for that research group, I did take the course in which researchers in the field are initiated into the vast topic.
The basic concept in superstring theory is that perhaps all known physical objects, i.e., photons, quarks, electrons, etc., and everything they make up, are different forms ["modes"] of a single type of string-like object at an incredibly small scale. That scale is in fact so small that it is 10,000,000,000,000,000- ten quadrillion [to those using the Queen's English ten thousand billion]- times smaller than what we can currently access. This inherently represents the problem; predictions of string theory, even apart from the fact that it can take many forms, are so far removed from what we are currently able to observe that no one knows how string theory would manifest itself in a laboratory situation. Because of this, every possible form of string theory has the same standing as every other possible form; one simply cannot know if and know it related to physical reality.
The goal of making string theory testable is hindered by practical issues, both physical and economic. A facility that accesses energies at the MeV scale costs a few million US dollars. A facility that accesses the GeV scale, i.e., energies about a thousand times more, costs a few billion US dollars. Facilities to access the TeV scale, i.e., energies about a thousand times more than that even, are being built and may end up costing a few trillion. Even if the money were available, no one currently knows even theoretically how to make facilities to access higher energies, let alone energies on the order of ten quadrillion times more.
New ideas in string theory can of course change this situation dramatically but until and unless such radically new and fundamental ideas are forthcoming in the field, one should not expect string theory to become testable experimentally.