Of course. Read the psionic class features carefully. Does using powers require concentration? You can't cast spells while raging because it requires concentration to do so.
Disregarding any possible Rage/Power incompatibility: Yes. You can multiclass with whatever you want, as long as the alignments don't conflict.
I have a question can you be a barbarian and a Psionic class ?
It depends. What psionics rules are you using? If you are using the 3.5 D&D Expanded Psionics Handbook (And presumebly the Psionics Unleashed book from DSP, which is based on the XPH), it says the following:
To manifest a power, you must concentrate. If something threatens to interrupt your concentration while you’re manifesting a power, you must succeed on a concentration check or lose the power points without manifesting the power. The more distracting the interruption and the higher the level of the power that you are trying to manifest, the higher the DC. (Higher-level powers require more mental effort.) When you make a concentration check, you roll d20 and add your manifester level and the ability score modifier used to determine bonus power points for that class.
While raging, a barbarian can't concentrate, and so can't manifest any powers.
But that's muddying the issue.
Whether or not he can use his powers while Raging is irrelevant.
He can multiclass with whatever he wants, there's no restriction except for PrCs.
If he wanted to make a psychic Barbarian who slings Psionics when not Raging he may do so with no issues.
