She should not fall within the degree of prohibited relationship. If she doesn't fall you can.

There are following relationship which are prohibited in hindu law marriage:

[ Degree Of Prohibited Relationship as per the Hindu Marriage Act, 1955] 
Mother. 
Father's widow (step mother). 
Mother's mother. 
Mother's father's widow (step grand-mother). 
Mother's mother's mother. 
Mother's mother's father's widow (step great grand-mother). 
Mothers's father's mother. 
Mother's father's father's widow (step great grand-mother). 
Father's mother. 
Father's father's widow (step grand-mother). 
Father's mother's mother. 
Father's mother's father's widow (step great grand-mother). 
Father's father's mother. 
Father's father's father's widow (step great grand-mother). 
Daughter. 
Son's widow. 
Daughter's daughter. 
Daughter's son's widow. 
Son's daughter. 
Son's son's widow. 
Daughter's daughter's daughter. 
Daughter's daughter's son's widow. 
Daughter's son's daughter. 
Daughter's son's son's widow. 
Son's daughter's daughter. 
Son's daughter's son's widow. 
Son's son's daughter. 
Son's son's son's widow. 
Sister. 
Sister's daughter. 
Brother's daughter. 
Mother's sister. 
Father's sister. 
Father's brother's daughter. 
Father's sister's daughter. 
Mother's sister's daughter. 
Mother's brother's daughter.

As you are not coming anyone of these category, so you can marry. This is legal in hindu law.

Under special marriage act the relationship is not prohibited, so you can marry under special marriage act. 

No it doesnt allow you. But secretly you can if your sister is in confidence. If you both love each other genuinely. Go settle abroad.

You cannot marry your first cousin it falls under prohibited degree of relationship 

Dear Concerned, 

No such marriage falls under the Degree of prohibited Relationship under the Hindu marriage act and such marriages are not allowed. MORE SO such marriage will call fall a great social challenges , hence it is advised not to get into such marriage. 

Additionally this marriage is prohibited by the Special marriage act as well.

IN CASE you are adamant for such marriage, you should consider, relocating with the girl to some other city / country where it would not matter who you are and what you background is ........

Best of luck.  

One of the specified condition for a valid marriage in The Hindu Marriage Act is that the groom and bride are not sapindas or within the degree of prohibited relationship. With reference to any person extends as far as the third generation (inclusive) in the line of ascent through the mother, and the fifth (inclusive) in the line of ascent through the father, the line being traced upwards in each case from the person concerned, who is to be counted as the first generation. Two persons are said to "sapindas" of each other if one is a lineal ascendant of the other within the limits of sapinda relationship, or if they have a common lineal ascendant who is within the limits of sapinda relationship with reference to each of them

All first cousins – paternal and maternal, parallel and cross – are placed by the Special Marriage Act in the category of prohibited marital relationship. Under the Hindu Marriage Act 1955 marriage with second cousins (father’s first cousin’s children) is also not allowed due to the restriction known as “sapinda” relationship. But, The Special Marriage Act 1954, however, does not place any second cousin in its two lists of prohibited degrees in marriage.

Degrees of prohibited relationship in Special Marriage Act

a man and any of the persons mentioned in Part I of the First Schedule and a woman and any of the persons mentioned in Part II of the said Schedules are within the degrees of prohibited relationship

Relationship includes,-
a) relationship by half or uterine blood as well as by full blood:
b) illegitimate blood relationship as well as legitimate;
c) relationship by adoption as well as by blood; and all terms of relationship in this Act shall be construed accordingly.

"Full blood" and "half blood"- two persons are said to be related to each other by full blood when they are descended from a common ancestor by the same wife and by half blood when they are descended from a common ancestor but by different wives.

"Uterine blood"- two persons are said to be related to each other by uterine blood when they are descended from a common ancestress but by different husbands.

"ancestor" includes the father and "ancestress" the mother; Solemnization of Special Marriages

So You cannot marry her.

Dear client,

Under special marriage act , inter caste marriage solemonized. And your marriage comes under prohibited relationship in both hindu and special marriage act.

This relationship is covered under the sapinda marriage which is not allowed and void ab initio but if it is allowed by the social system and accepted in the society then only you can go ahead with this marriage while going for the registration you have to give affidavit in this regard that both of you are not in the sapinda relationship

Special marriage act is applicable only when both people belong to different religion.

And hindu marriage act allowsmarriage with father's sister's daughter.

This is not considered as legally valid 

This may fall under. Sapinda relationship, hence the marriage would be null and void.