What do you mean by Record ID? Is this the number of the row? If this is the case, you can add a new Field and call it Record ID, set it to Autonumber. Then in Table 2, set the Field where you want to see this number to Lookup this number.
Perhaps I’m missing something obvious, but isn’t that precisely how Table 2 is linked to Table 1? By the record ID?
If you enumerate the records of Table 2 using the API and look specifically at the field that links to Table 1, you will see record IDs - these are the actual record IDs of Table 1 (I think without seeing your data or a diagram).