Shirley MacLaine shimmers and shakes in Broadway solo show; Shirley MacLaine on Broadway. Staged and choreographed by Alan Johnson.

It's easy to think of Shirley MacLaine - ex-gypsy, ingratiating entertainer, author, Oscar winner - in terms of endearment. Returning to the scene of her first leap from obscurity, Miss MacLaine has brought a 90-minute, Las Vegas-like act to Broadway's Gershwin Theatre for a limited engagement. If ''Shirley MacLaine on Broadway'' opts for glitter and flash rather than high style, its heart is in the right place for this kind of crowd pleaser. The show's attitude might be summed up in the Jule Styne ''Gypsy'' anthem, ''Let Me Entertain You.''

And entertain she does. Besides strutting her stuff as a dancer, Miss MacLaine sings, revisits scenes from several film roles, reminisces amusingly, philosophizes lightly, quotes T.S. Eliot and George Bernard Shaw, and displays her Oscar. From her grand-style entrance in a sequined red pantsuit to her finale in a sequined black evening gown, she commands the scene and the situation. She is lithe, graceful, winsome, and impish, a versatile performer with the haunting face of a clown.

Miss MacLaine is backed by four agile dancers and a solid onstage band. In a big ensemble number, the star and her troupe bound into a series of routines in which director-choreographer Alan Johnson parodies and pays tribute to certain eminent contemporaries: Bob Fosse (snapping fingers, pelvic thrusts, white gloves, black derbies); Michael Kidd (athleticism and acrobatics); black choreographers like George Faison, Billy Wilson, and Geoffrey Holder (here credited with having introduced a whole new way of moving). The sequence ends in calculated disarray. Meanwhile, ''Sweet Georgia Brown,'' under conductor Jack French, has seldom undergone a more strenuous syncopated workout.

Among the show and pop tunes making up the eclectic score, ''Life Is Just a Bowl of Cherries'' (and its corny preface) proves one of the more winning. Composers (and their lyricists) called upon in the course of the entertainment include Cy Coleman, Ray Henderson, Harold Arlen and George Gershwin in an amusing couterpoint, Vincent Youmans, and Richard Rodgers. For her finale, Miss MacLaine sings Rodgers and Hammerstein's ''A Cockeyed Optimist'' and John Lennon's ''Imagine.'' Marvin Hamlisch and Christopher Adler have provided origigal music and lyrics, and there is ''additional material'' by Larry Grossman and Buz Kohan.

The show was lighted by Ken Billington and costumed by Pete Menefee. The only jarring note is raucous overamplification, which mars the pleasure of some numbers.