The 'Whip It' star signed up to the social media site yesterday, admitting she is "late to the party".
She tweeted: "Late to the party, but happy to be here. 140 characters should keep me from rambling... Someone told me it doesn't all have to fit in 1 tweet. (sic)"
Drew, 38, chose a picture of her on the cover of InStyle magazine as her backdrop and also re-tweeted news she will be hosting a Twitter chat with the magazine this week.
By Wednesday morning she had amassed over 25,000 followers.
Drew - who is married to Will Koppelman, with whom she has 10-month-old daughter Olive - has said she wants to have more children, and could use the social networking site to share bulletins from her daily life such as her cravings, should she fall pregnant again.
While she was due to have Olive, the Hollywood star has told how she was hungry for calorie packed treats.
She said: "I loved cheeseburgers. I wanted nothing to do with vegetables and I love vegetables! And ice cream disgusts me, but all I wanted was Thrifty Mint 'n Chip ice cream.
"I gained about 40 lbs. I think I gained an extra five the last week because I was so late and was like, 'Forget it! All bets are off! I'll have two cheeseburgers.' "
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