Can I claim my son for the time he was living with me and he was working.

I assume what you mean is: can you claim him as a dependent on your tax return - is that right? The rule for claiming your son as a dependent is that he must satisfy the requiremenst of either being a "qualifying child" or a "qualifying relative." The rules are different for each:

1. To be a qualifying child he must be under 19 years of age, or a full time student under age 24, he must have lived with you for at least half the year, and he must not have provided more than half of his own support during the year.
2. If he he is not a qualifying child, he may then fall into the category of qualifying relative if his gross income is less than $3,300/year, and if you povide more than half of his support during the year.

In other woirds, if your son earned more than $3,300 you can not claim him as a dependent.

IRS Pub 501 provides details:

Publication 501 (2006), Exemptions, Standard Deduction, and Filing Information