Sentinel 1 products do not use a a tile grid. However, to identify products over your polygon you can use one of several Sentinel 1 search/download resouces. This is not an exhaustive list by any means.
ESA offer the SciHub which allows searching by drawing a polygon area of interest (AOI). You have to create an account (free) before you can search and download the products. A User Guide is also available.
The Alaskan Satellite facility's Vertex tool is another good resource and allows you to draw an AOI or enter specific coordinates. They provide interactive tours of the tool.
Alternatively, ESA do provide information on the Sentinel 1 acquisition segments in KML format - you could download the segment for the dates you are interested in and view alongside your AOI.
If you still want to download via AWS these resources will give you enough information about the products over your AOI to enable you to find them on AWS.
GitHub user Kersten has put together a list of all things Sentinel, including more resources.