While I agree with the first answer for the most part, you don't really see the iambic beat until the second line. If you read the first line as "Drink TO me ON-ly WITH thine EYES," the reading will sound very forced. Although the poem has a predominantly iambic meter, it is important to realize that good poems, such as this fine example by Ben Jonson, do not have the perfectly regular rhythm we associate with nursery rhymes or greeting card verse. It is the variations that help convey the meanings.
The opening beat of the first line is "DRINK to me," with is a dactyl (waltz-like or ONE-two-three). Similarly, a good reader with use a spondee (two successive heavy beats) in reading the phrase "THINE EYES." So the meter is predominantly iambic, but the poem definitely does not open with a distinct iamb.
And because Jonson placed these lines as he did, there is no reason to take the two lines together and consider them "heptameter." Rather, the alternating pattern of tetrameter with trimeter is commonly found in poems that are put to music. The poem "To Cecilia" provides the lyrics for an art song that you may not be familiar with but that was well-known for decades. The song goes by the first line, "Drink to me only with thine eyes," attributed by some sources to Colonel R. Mellish (1777-1817), though there is some controversy regarding this attribution. Its tune can be found online. (See the second link below.)
In the poem "Song: To Celia," Ben Johnson uses as iambic meter, or syllabic beat, changing every other line between four and three iambs (if these lines are considered together, it could be called heptameter, where the author uses seven iambs per line). An iamb is one type of "foot" in poetry, each iamb made up of two syllables, with the emphasis on the second.
That means, in the first line of the poem (and every other odd numbered line thereafter), there are eight syllables, forming four iambs, with the first syllable unstressed and the second stressed, or accented. In the even numbered lines, there are six syllables, forming three iambs. Note the stressed syllables in bold:
DRINK to me only with thine eyes,
And I will pledge with mine;
Or leave a kiss but in the cup
And I'll not look for wine.
The thirst that from the soul doth rise
Doth ask a drink divine;
But might I of Jove's nectar sup,
I would not change for thine.
The rhyme scheme he uses is ABCBABCB, meaning that lines 1 and 5 rhyme; lines 2, 4, 6, and 8 rhyme; and lines 3 and 7 rhyme. He maintains this same meter and rhyme pattern in the second stanza as well.