When using these tabix files, note that you'll need to translate your chromosome numbering scheme to accession identifiers from the NCBI Reference Sequence Database (RefSeq), e.g. 1 becomes NC_000001.11:
% tabix https://ftp.ncbi.nlm.nih.gov/snp/latest_release/VCF/GCF_000001405.38.gz NC_000001.11:727841-727841
NC_000001.11 727841 rs1339480271 G A . . RS=1339480271;dbSNPBuildID=151;SSR=0;GENEINFO=LOC100133331:100133331;VC=SNV
You could download the gzip file and its associated tbi index file to run tabix locally, and then use awk or other scripted approaches to read through your list of SNPs, writing out the rsID.