Yes, it is possible, but once you append the data to another table you effectively lose the connection to the ODBC source. In other words, if data in the source changes, it would not be reflected in the data in your table.
If that is OK with what you are doing, then you need to create the new table that will hold the data. Then change the type of your current query to an append query, select the new table name, correlate the fields of the query to the corresponding ones of the table and then run the query.
You mentioned that there are too many records in your query. Can't you use some criteria to filter the results down to what you need?