How can I preprocess text to feed into a SVM?
X needs to be the features for your Model and Y needs to be a target variable.
As you mentioned, you are using a IMDB dateset so, all the features which you want your model to use will be stored in X variable whereas the 'LABEL' columns will be stored in the Y variable.
Instead try this code:
X = vectorizer.fit_transform(df_train['text'])
Y = vectorizer.transform(df_train['label'])

classifier_linear = svm.SVC(kernel='linear')
classifier_linear.fit(X, Y)

Another thing you did wrong here was that,
you passed the target variable of you testing data.
You train your model from your training data and if you are confident enough on your model then you test it using the testing data.
Concepts which can help you: Cross-Validation, train_test_split.