The answer to this question is more complex than it should be.
If your arbitration clause is governed by the Texas Arbitration Act, then an interlocutory appeal is allowed where there has been an order denying a motion to arbitrate or granting an application to stay an arbitration. (CPRC 171.098) However, under that act, orders compelling arbitration are generally not appealable by way of interlocutory appeal. If the trial court actually dismisses the case after compelling arbitration, that action is appealable, as it is a final judgment. Childers v. Advanced Foundation Repair, L.P., 193 S.W.3d 897 (2006). If the trial court merely stays the case, there is no basis for an appeal at that time. However, some courts have said that mandamus is available in that situation. In re Godt, 28 S.W. 3d 732 (Tex. App.--Corpus Christi 2000, no pet.)
In cases governed by the Federal Arbitration Act (9 U.S.C. 2, et. seq.), interlocutory appeal is not available, but rulings denying arbitration are reviewable by way of mandamus. In Re D. Wilson Constr. Co., 196 S.W. 3d 774 (Te. 2006). However, where a trial court has granted a motion to arbitrate, and has not dismissed the case (but rather stayed it), the weight of authority is that no mandamus is available and that appellate review must await the entry of a final judgment. In re Gulf Exploration LLC, 289 S.W. 3d 836 (Tex. 2009).
Thus, given the policy favoring arbitration that has prevailed in recent decades, these holdings reflect a preference for quick appellate review of orders denying arbitration, but with regard to orders compelling arbitration, "not so much."
How do you know whether your case is governed by the Texas or the federal arbitration act, or perhaps by both? That will be the subject of another blog entry in the near future.