In humans, the hormone testosterone enters cells and binds to specific proteins, which in turn bind to specific sites on the cells' DNA. What is the function of these proteins?

As a transcription factor

Explanation:

Testosterone is a male sex hormone secreted by the testicles which promote the growth of the male reproductive organs and the male characters like muscle buildup.

The hormone shows the paracrine effect and thus act on the target cell at distant. The mechanism of action of the testosterone is that it controls the gene expression of various other genes.

The testosterone binds the specific proteins which activate the expression of the gene that is they acts as a transcription factor which activates the expression.  

Thus, as a transcription factor is correct.