Is there a read mapper that allows input in SAM format instead of FASTA/FASTQ?
The common solution for scRNA-seq is to put cell barcodes and such in read headers and then post-process things with UMItools.

But regarding your actual question, STAR can accept SAM/BAM as input with the --readFilesType SAM PE option (it's SAM for both that format and BAM). You can swap SE for PE if your data is single-end (or is effectively that way, as is the case in many scRNA-seq experiments). Note that in the case of PE experiments that mates must be next to each other. I really don't know what this does with auxiliary tags though, so you would need to see if they're lost before you start processing a lot of data).