Which line of Emily Dickinson's "A Bird came down the Walk" marks the poem's climax?

This is a matter of interpretation. We could offer different lines as candidates for the climax, or we could claim that there are multiple ones, or none.

Personally, I'm not convinced that the poem contains enough of a standard story structure to really have a specific climax, but we can make some interesting guesses.

Looking for the most exciting or most tense part of the poem, you might say that this line is the climax:

"I offered him a Crumb"

There, the speaker moves from simply observing the bird to actually reaching out and trying to interact with it, which in the universe of the poem is a major upheaval.

Alternately, the climax could be here:

"And rowed him softer home—"

In that line, the bird leaps into beautiful motion after having only made small movements on the ground. There's the action of the bird suddenly revealing its grace and power of locomotion (and not just its skill in eating or looking around) which could be interpreted as the most important, most tense moment.

Let's take a different approach, also. The fact that the poem has five stanzas invites consideration: does each stanza match up with the five main sections of a typical story, like a Shakespearean play often does with its five acts? If so, then we should find the climax in the third stanza (and the exposition in the first, the rising action in the second, the falling action in the fourth, and the resolution in the fifth). Looking into the third stanza, here's an option for the most exciting line:

"They looked like frightened Beads, I thought—"

It's here that the speaker realizes that the bird appears to be scared, which is one of her most intense and human observations of the creature. Is it the true climax? Again, we can't say for certain.