The correct option is
A haven't read a newspaper
The present perfect tense is used to describe something that happened in the past, but the exact time it happened is not important. It has a relationship with the present. Since, this sentence is concerned with something that has happened, we would be using present perfect tense.
Have/has + past participle makes the present perfect.
Now since, the whole sentence is in the first person, we would be using "have" and not "has". Now, the second part of the sentence is in the negative form, this makes it "haven't"
("have" is used in case of first and second person framed sentences.)
Now, for the past participle, it the form of a verb, typically ending in -ed in English, which is used in forming perfect and passive tenses and sometimes as an adjective. In this case the past becomes, "read"
Option A is correct.