The two ends of my gene have same restriction sites. And the destination vector also has two same sites. Can I clone the gene directly to the destination vector? I know it's possible that the gene can be reversed, but did anyone do this before?
Yes, you can do exactly what you have planned. You'll just have to use PCR or sequencing to find the clones where your gene faces the correct direction.
PCR amplification of the plasmid using an insert specific primer paired with a vector specific primer can be designed to produce an amplicon of a specific size only if the insert is in the correct orientation.
An other way for screening clones is to perform plasmid prep on transformant clones and to double digest the plasmids with a plasmid backbone specific cut and an insert specific cut (provided the latter is not right in the middle of the insert). Digest pattern on agarose gel will tell you what the orientation of the insert is toward the plasmid backbone.
You can surely do restriction digestion with a single RE whose sites flank your insert and accordingly clone it into a destination vector via the same site. However you may face some problems
1. The vector may recircularise and give you false positive colonies after transformation, which can only be verified after screening.
2. The insert may flip in the construct (this is pretty much common) thereby affecting your downstream procedures.
To circumvent the above problems. you can dephosphorylate the vector using commercially available Alkaline phosphatases. This can be achieved simultanously while you digest the vector. By doing this, the chances of plasmid recircularisation are very low.
To verify the correct orientation of my insert, I normally perform colony PCR using the insert specific forward primer and vector specific reverse primer or vice versa. Positve clones can be further verified using restriction digestion and sequencing following plasmid extraction.