Did you try the JASPAR database and check the sequence with your SNP and without to see any differences?

A commonly used experimental approach to identify transcription factors binding a known DNA sequence would be yeast one-hybrid, using your promoter as bait. Of course, this would identify a set of transcription factors that can bind in vitro, and then you would have to screen through the candidates to see if the SNP affected activity, possibly using a luciferase reporter assay.

If the region can easily be broken down into fragments of a few hundred basepairs (e.g. by PCR) to be radiolabeled as probes, old-fashioned gel mobility shift and DNase or methylation interference footprinting with nuclear extract from your cell type of interest would give you an idea of where factor binding sites might be.  The footprinted sequences, or regions delimited by mobility shift assays with increasingly smaller probes, can help to identify the cognate factors.

Alternatively, you can label the promoter fragment with biotin, perform a DNA pull down with protein lysates from your cells/organism and perform an MS/MS experiment. In our  hands this worked pretty well. Just make sure you have the appropriate negative controls. (for more information check this publication out: Cell Rep. 2013 Dec 26;5(6):1611-24. doi: 10.1016/j.celrep.2013.11.021. Epub 2013 Dec 12.) Good luck

In my lab, we usually use the EMSA kit (https://www.piercenet.com/instructions/2160919.pdf) with the oligo is your paticular region of promoter - label with biotin, incubate it with all the protein complex extract from cell nucleus ( you should choose the cell line that your gene is well express in). If then you see a band shift of DNA oligo - protein complex then you try to separate the protein complex and send them to MS to see if there is any of the proteins is transcription factor.

Hope it helps.