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I think you'd want the reverse, which is indeed elementary: if f halts then you get a circle-free TM, but if f does not halt then you get a non-circle-free TM. This can be done by

  f(); while(1) output_digit(0);

or any number of other simple constructions. This is because a circle-free TM always reaches a certain pre-defined event (output_digit), much like a halting TM. But a non-circle-free TM might forever fail to make progress, in a way that you can't necessarily tell if it's stuck or will eventually output another digit, much like a non-halting TM.

Edited to add: also Turing proved that the symbol-printing problem is undecidable, as the authors of this paper describe: will a Turing machine ever print a certain symbol? If you name the symbol in question "HALT" then this is almost identical to the halting problem, and easily reducible in either direction.