He vowed to give charity every time he committed a sin, then he committed sin but did not give charity

Firstly: 

Making vows so that one will not commit sin is something that
was done by some of the salaf, in order to punish themselves and train
themselves not to commit sin, but that was with regard to things that thy
were able to do. 

Harmalah said: I heard Abu Wahb say: I vowed that every time
I backbit about a person I would fast for a day and that wore me out,
because I used to backbite and fast. So I intended that every time I backbit
about a person I would give a dirham in charity instead, and because of my
love of money I gave up backbiting. 

Al-Dhahabi said: This, by Allaah, is how the scholars were.
This is one of the fruits of beneficial knowledge. 

Siyar A’laam al-Nubala’, 9/228 

It is better for a Muslim to refrain from committing sin
without making vows or oaths, so that he will not expose himself to breaking
that oath or not fulfilling that vow. 

Secondly: 

If the one who makes a vow intends to prevent himself from
doing a particular deed, then either he will break that vow or he will not.
If he does not break it then he does not have to do anything. If he does
break it then he is given the choice of two things: either to fulfil the vow
or to offer kafaarat yameen (expiation for breaking a vow).   

Ibn Qudaamah said in al-Mughni (13/461): 

If he makes a vow to prevent himself or someone else from
doing something, or to encourage him to do something, such as saying, ‘If I
speak to Zayd, then I am bound to perform Hajj, or give my wealth in
charity, or fast for a year,” this is a vow and the ruling is that he has
the choice between fulfilling what he swore to do, in which case he does not
have to do anything else, or breaking his vow. So he has the choice between
doing what he vowed to do or offering kafaarat yameen. This is called a vow
of desperation and anger, and he does not have to fulfil it. This is the
view of ‘Umar, Ibn ‘Abbaas, Ibn ‘Umar, ‘Aa’ishah, Hafsah and Zaynab bint Abi
Salamah. It is also the view of al-Shaafa’i. 

Shaykh Ibn ‘Uthaymeen was asked: 

I am a young man who was negligent then Allaah guided me, but
I still commit some sins. I have tried to repent from them many times but I
could not. I said to myself that I should vow that if I repeated this sin, I
would fast for two consecutive months. But the Shaytaan tempted me and I
said that the vow in this case is like a yameen (oath) for which kafaarah
(expiation) may be offered. Then I committed that sin again. What should I
do, may Allaah reward you with good? Is it permissible for me to feed sixty
poor persons, because that is easier for me than fasting? Please note that
Allaah has blessed me by helping me to repent from this sin now. 

He replied: 

Firstly: A Muslim should be determined, resolved and strong
in resisting haraam things without swearing oaths or making vows, and he
should do what he is obliged to do without swearing oaths or making vows.
Allaah says (interpretation of the meaning): 

“They swear by Allaah
their strongest oaths, that if only you would order them, they would leave
(their homes for fighting in Allaah’s Cause). Say: Swear you not; (this)
obedience (of yours) is known (to be false). Verily, Allaah knows well what
you do”

[al-Noor 24:53]

But some people may be incapable of controlling themselves so
they resort to vows and oaths to make themselves do what they are obliged
to, or to refrain from doing haram things. The scholars (may Allaah have
mercy on them) mentioned that the vow which is intended to help one to
refrain from something haraam or do something obligatory comes under the
ruling of a yameen (oath). Hence the brother who asked this question has to
offer kafaarat yameen as an expiation for this oath, by feeding ten poor
persons, giving each one of them a mudd (or two handfuls) of rice or wheat,
or clothing ten poor persons, or freeing a slave. He has the choice of doing
one of these three things. If he cannot do any of them, then he has to fast
for three consecutive days, because Allaah says in Soorat al-Maa’idah
(interpretation of the meaning): 

“Allaah will not punish
you for what is unintentional in your oaths, but He will punish you for your
deliberate oaths; for its expiation (a deliberate oath) feed ten Masaakeen
(poor persons), on a scale of the average of that with which you feed your
own families, or clothe them or manumit a slave. But whosoever cannot afford
(that), then he should fast for three days”

[al-Maa’idah 5:89]

With regard to feeding the poor, it is permissible to make
food, lunch or dinner, and invite ten poor people to come and eat. 

Fataawa Islamiyyah, 3/501.