There is no database ID for ad-hoc queries. You could try parsing the statement and figuring out which tables it uses and which DB those are in.
But then, what database should this be associated with?
SELECT * FROM db1.dbo.table1
Or this one
FROM db1.dbo.table1 t1 inner join db2.dbo.table2 t2 on T1.SomeID = T2.SomeID
Edit: Or you might be able to parse it out of the query plan, if you're familiar with XML.
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