I'm sure others can answer more thoroughly but the lyrics of this song (though there seem to be many versions) all speak to either a longing for home or an expectation of being home soon.

Two examples: "She's logging sixteen as she speeds from the South, A wind in her royals, a bone in her mouth, With a wake like a millrace she speeds on her way, For the girls have got hold of her tow-rope today."

And,

"The Old Man he stood on the poop at high-noon, He paced fore-and-aft and he whistled a tune, Then he put by his sextant and this he did say: "The girls have got hold of our tow-rope today."

The Royals are among the highest sails on a ship and would only be set if the ship were making all possible speed. Likewise having a "bone in her mouth" refers to the white foam thrown off the bow of a fast moving ship. In the second example the sextant is being used to check the ship's current location and affirm home is close.

So In both of these cases the song is being aspirational, suggesting that if all efforts are made, then the girls WILL have hold of the ship's tow ropes as it comes in to dock.

So to the core of your question, the tow ropes are the lines that would either be tossed from the ship to the dock to pull her in, or these lines could be rowed ashore in smaller boats with the same purpose in mind.

More details on that here.

https://www.reddit.com/r/AskHistorians/comments/1katgo/how_did_ships_dock_during_the_age_of_sail/?utm_medium=android_app&utm_source=share

[EDIT] It occurs to me that another plausible interpretation of the lyrics is that rather than aspirational, they could be suggesting that these men's loved ones back home are literally "towing" the ship forward through the power of prayer or force of will.

I don't think these two interpretations are mutually exclusive.