Is it acceptable to list unpublished papers in a PhD application for computer science?
Yes, this is done routinely; provided, however, that these papers are clearly marked as "currently under peer review" or "submitted for review" and specify the journal. If the paper has passed peer review and us merely awaiting publication, it can be marked as "to appear." If the paper has not passed peer review,  it should not be labeled as "to appear." 

Best regards and wishing a swift publication process.