(I'm not a native speaker of English, so I turned to dictionaries)
Damkerng's walk <somebody> home seems to be a great option.
Thanks to his suggestion, I recalled "I'll see you home", built along the same lines but allowing for the possibility that the girl will reach home not by foot but, say, by train or tram.
This phrase has been in use for a long time:
The fair was over, night was come,
The lad was somewhat mellow,
Says he, 'my dear, I'll see you home',
I thanked the charming fellow.
We trudged along, the moon shone bright,
Says he, 'If you'll not tell-o,
I'll kiss you here by this good light',
Lord, what a charming fellow!
(The Agreeable Surprise, John O'Keeffe, 1795)
Another option (but see the comment by mattdm below):
I will accompany you.
Could you please accompany me?
There is also the old-fashioned term "chaperone", but that is usually applied to old dames accompanying ladies, not to men.
Yet another option:
come along - to accompany someone who leads the way.
asked me to come along on the trip
In cases like this, it's usually nice to google for synonyms. There are a number of thesaurus sites on the web. Here's a thesaurus entry for accompany.