US branch for European company
This USA branch or new LLC will deal with clients, Romanian origin and not only, for official translations, those clients shall pay these services in a bank account opened with some American Bank.
The possibility of branching your Srl company into the U.S. is indeed a possibility, but in all honesty the time, money, resources and headaches involved would by far and away exceed the measures and simplicity in opening a new company. If you are the only member, or part of a small 2 or 3 member partnership, then I would suggest opening an LLC. If you have a large amount of members, then a Corporation might serve your needs more.
California is not the most business-friendly state. The regular state's filing time for new business entities can exceed 3 months, which is amongst the longest in the country, but its possible to expedite it to 3-4 weeks. Upon forming a new business, there are numerous other filings and fees required by the state (including a statement of information upon the company formation, and an annual $800 franchise tax) that increase the start-up and maintenance costs.
If your company plans on providing it's services through an online website, incorporating your business in states such as Wyoming or Delaware would be far more practical as the initial start-up fees along with the annual maintenance fees would be much cheaper. These states also have some pretty enticing tax advantages as well.
As for the company's bank account, you can get an Apostille attached to your American business paperwork (as Romania is a signatory of the Hague Convention) allowing you to open the company bank account in your home country of Romania. However, to open your business account here in the United States, you will probably have to physically come here to accomplish this.
Also keep in mind, whichever state you decide to incorporate in, you will be required to maintain a Registered Agent. This is a physical name and address in the state of the business' formation to receive service of process from the Secretary of State office. This is a service we provide in every state as most international business owners would not have an address here in the United States.
I hope you found this answer to be of some assistance.