For people who are not used to command line, biomart has a very nice interface for downloading SNPs etc. Go to http://www.ensembl.org/biomart/martview/ . You can filter based on gene IDs, you will find these on ensembl/UCSC.
Get all SNP
rs* IDs via the command line:
$ mysql --user=genome --host=genome-mysql.cse.ucsc.edu -A -N -e 'SELECT chrom, chromStart, chromEnd, name FROM snp142Common' hg19 > snp142Common.bed
Get genes and convert to BED with
$ wget -qO- ftp://ftp.sanger.ac.uk/pub/gencode/Gencode_human/release_19/gencode.v19.annotation.gtf.gz \ | gunzip -c \ | grep -w "gene" \ | gtf2bed \ > genes.bed
Adjust this step for whichever annotations you use or prefer.
Filter gene names for the gene of interest, then map SNPs to gene, using
bedmap to look for SNPs whose positions overlap those of Gencode genes:
$ grep -w 'name-of-gene' genes.bed | bedmap --echo snp142Common.bed - > answer.bed