Although adopted siblings wishing to marry is an extremely rare and unusual situation, it may possibly come up. The quick answer to the question about adopted siblings marrying one another is "no." In some rare instances, there may be exceptions.
It appears that throughout the U.S. and in most of the world, parties that are in a prohibited relationship such as direct descendants or siblings, including adopted (by law) relationships are not allowed to marry.
In most locales, it is commonly believe that "as long as two individuals have two common parents, they are considered full siblings, regardless if they have been adopted" according to the website Genopro.com.
The wording of the Colorado statute regarding prohibitive relationships does not include the word "adopted," so adopted siblings who want to marry one another may want to check further with a county clerk there.
There are several articles on Wikipedia on the topic including, Laws Regarding Incest, which discussed laws across the world. Some may still view adopted siblings as full siblings nonetheless and see any sort of relations between them as incestuous. Dictionary.com defines incest as "sexual relations between closely related persons. There is no specification about blood relation in the definition.
For more specific information about laws in the U.S., read Laws Regarding Incest in the United States. This article states that the laws vary widely between jurisdictions in regards to both the definition of the offense and the penalties for violating the laws.
According to StarsofDavid.com, "Theoretically there is no prohibition to marriage between adopted siblings. In fact, one such case is described in the Talmud. However, most authorities would forbid such a marriage because of unseemliness."
The assumed reason for these laws prohibiting marriage between adopted siblings is to prevent creating perceived "family chaos." It is likely that your parents would loudly object to such a union.
It is a much better idea to never enter into a romantic relationship of any sort with and adopted sibling, even if this person came into your life later in childhood.
On a side note, this issue has been in the news recently. In the case of Bobbi Kristina Brown and Nick Gordon, Nick came into the picture as an older child. Bobbi claims that her famous, and now deceased mother, Whitney Houston, was permissive about the union. Regardless, they received a significant amount of backlash and criticism for marrying...or at least saying they were married. The two were supposedly never married legally. It is doubtful they would have been able to legally marry either. Bobbi died tragically during the summer of 2015. Here partner, Nick, has been implicated in her death.
The bottom line is that no, siblings, whether by blood or adoption, can not legally marry nor should they.