The passage you remember is from act 1, scene 4, of Romeo and Juliet. The exact lines you refer to are spoken by Romeo to his good friend Benvolio as they are about to enter the Capulet feast. Romeo does not wish to attend and is uneasy; entering the stronghold of their family’s worst enemy is not something to take lightly! Romeo has a strong sense of foreboding, and he muses:

I fear too early, for my mind misgives
Some consequence yet hanging in the stars
Shall bitterly begin his fearful date
With this night’s revels, and expire the term
Of a despisèd life closed in my breast
By some vile forfeit of untimely death.

Romeo understands that attending the feast is akin to crossing a threshold that leads to events outside of his control. The fact the he references the possibility of an “untimely death” demonstrates that he understands the danger of the family feud between Montague and Capulet.

In this moment, Romeo could have opted to change course. Obviously, he doesn’t, and when he utters the lines you remembered—“But he that hath the steerage of my course / Direct my sail. On, lusty gentlemen”—he abandons his fears and proceeds with his plan to attend the Capulet feast. It is here that he will meet Juliet. At the end of the play, one can see that Romeo’s comments in this scene were clearly prescient and serve as foreshadowing for the tragic events later on in the play.

It's from Romeo and Juliet, Act 1, Scene 4 - the 'Queen Mab' scene, right at the end, before the scene changes to the Capulets' party.

Romeo brings an end to the 'Queen Mab' argument between him and Mercutio about dreams and how far they can foreshadow real-world events by ominously foreseeing 'some consequence yet hanging in the stars', some bad event, which he thinks will begin 'with this night's revels'.

But he finally concludes to let the person who can 'steer' his course direct his sail: whether he is encouraging Benvolio or another of the Montague boys to lead him to the party, or whether he is referring to a supernatural force 'steering' his 'course' is ambiguous.

It is. It is from "Romeo and Juliet."You'll find it in Act I, scene 4. In context, it looks like this: "I fear, too early: for my mind misgives
Some consequence yet hanging in the stars
Shall bitterly begin his fearful date
With this night's revels and expire the term
Of a despised life closed in my breast
By some vile forfeit of untimely death.
But He, that hath the steerage of my course,
Direct my sail! On, lusty gentlemen." Romeo says it, and it is a way of foreshadowing the dark end to which his love will come.