The development of image time series retrieval (ITSR) methods is a growing research interest in remote sensing (RS). Given a user-defined image time series (i.e., the query time series), ITSR methods search and retrieve from large archives the image time series that have similar content to the query time series. Existing ITSR methods in RS are designed for unimodal retrieval problems, relying on an assumption that users always have access to a query image time series in the considered image modality. In operational scenarios, this assumption may not hold. To overcome this issue, as a first time in RS we introduce the task of cross-modal text-image time series retrieval (text-ITSR). In detail, we present a self-supervised cross-modal text-ITSR method that enables the retrieval of image time series using text sentences as queries, and vice versa. We focus our attention on text-ITSR in pairs of images (i.e., bitemporal images). Our text-ITSR method consists of two key components: 1) modality-specific encoders to model the semantic content of bitemporal images and text sentences with discriminative features; and 2) modality-specific projection heads to align textual and image representations in a shared embedding space. To effectively model the temporal information in the bitemporal images, we exploit two fusion strategies: i) global feature fusion (GFF) strategy that combines global image features through simple yet effective operators; and ii) transformer-based feature fusion (TFF) strategy that leverages transformers for fine-grained temporal integration. Extensive experiments conducted on two benchmark RS archives demonstrate the effectiveness of our method in accurately retrieving semantically relevant bitemporal images (or text sentences) to a query text sentence (or bitemporal image). The code of this work is publicly available at https://git.tu-berlin.de/rsim/cross-modal-text-tsir .