Wordorigins.org

This term arose in engineering circles. The earliest known usage is from 1910, in H.H. Suplee’s Gas Turbine:

It has therefore been thought desirable to gather under one cover the most important papers...In the present state of the art this is all that can be done.

There is a somewhat older use of status of the art dating to 1889 in Anthony’s Photography Bulletin:

The illustrations give a good idea of the present status of the art in the various methods of printing.

(Source: Oxford English Dictionary, 2nd Edition)