If DNA is the input, what is the output?
The central dogma of molecular biology states that DNA encodes the information for building proteins, the information is copied to messenger RNA through transcription, and messenger RNA is used to build proteins through translation. DNA is also copied through replication.

So while it's true that DNA contains the information needed to build a living organism, I don't think it can described as "turing tape" If I understand turing machines correctly, you have a string of 1s or 0s, and a machine reads this string. Based on rules provided by an instruction set the machine can set positions on the tape to 1 or 0. The analogy with DNA fails because DNA does not have a separate instruction set and cannot be written to. DNA produces RNA and DNA with the help of many many proteins and other molecules, all tightly regulated to coordinate replication of the genome and to produce the right amounts of RNA and protein at the right times. DNA can mutate when replication makes an error, but this is accidental, not comparable to turing machines.

If you're interested in how DNA might be used like a computer, there are several articles on DNA Computing, though you'll have to sort through those papers because many look like they just used a computer to analyze DNA.