It seems to me that, to be efficient, you need to 1) generate a random number between 0 and one less than the number of database records, and 2) be able to select the row at that position. Unfortunately, different databases have different random number generators and different ways to select a row at a position in a result set - usually you specify how many rows to skip and how many rows you want, but it's done differently for different databases. Here is something that works for me in SQLite:
select * from Table limit abs(random()) % (select count(*) from Words), 1;
It does depend on being able to use a subquery in the limit clause (which in SQLite is LIMIT <recs to skip>,<recs to take>) Selecting the number of records in a table should be particularly efficient, being part of the database's meta data, but that depends on the database's implementation. Also, I don't know if the query will actually build the result set before retrieving the Nth record, but I would hope that it doesn't need to. Note that I'm not specifying an "order by" clause. It might be better to "order by" something like the primary key, which will have an index - getting the Nth record from an index might be faster if the database can't get the Nth record from the database itself without building the result set.