Yes, "The Silken Tent" is most definitely a sonnet--and I didn't realize that Robert Frost wrote sonnets!
The poem has all the elements of a Shakespearean sonnet:
a) 14 lines;
b) iambic pentameter: each line contains five repetitions that "move" in a dah-DAH-dah-DAH pattern;
c) the rhyme scheme is abab cdcd efef gg.
The poem consists of an extended metaphor, sometimes known as a "conceit." The poet's lover is compared to "silken tent" that has been set up in a field.
The tent's "supporting central cedar pole" seems to stand almost by itself, without the help of "any single cord." This "signifies the sureness of the soul"--the lover's confident self-reliance. The poem's original title was “In Praise of Your Poise.”
The lover is independent but not aloof. She is
By countless silken ties of love and thought
To every thing on earth
Although Frost uses the sonnet, a very old form of poetry, his language in the poem is simple and modern.