There is nothing special about ₹ (the U + 20B9 New Rupee character), except that, being so new, it has almost zero font support. If you have a database connection that supports Unicode, you can save it as easily as any other character:
INSERT INTO Currency (name, symbol) VALUES ('INR', '₹');
(You would like to use NVARCHAR for storage and N'₹' in SQL Server.)
If you don’t have a Unicode-safe connection (for example, you are using some kind of crap tool, such as the Windows console), you will have to work around this using, for example.
VALUES ('INR', CHAR(226, 130, 185))
for a UTF-8 delimited column in MySQL or NCHAR(8377) for a Unicode column in SQL Server.
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